# Find the Roots (Zeros) 2x^5-2x^4-6x^3+6x^2-8x+8=0

Factor the left side of the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Regroup terms.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Let . Substitute for all occurrences of .
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Replace all occurrences of with .
Rewrite as .
Factor.
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Remove unnecessary parentheses.
Rewrite as .
Let . Substitute for all occurrences of .
Factor by grouping.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Replace all occurrences of with .
Rewrite as .
Factor.
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Remove unnecessary parentheses.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Apply the distributive property.
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by .
Reorder terms.
Factor.
Factor.
Rewrite in a factored form.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Remove unnecessary parentheses.
Remove unnecessary parentheses.
Divide each term by and simplify.
Divide each term in by .
Simplify .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify terms.
Combine the opposite terms in .
Reorder the factors in the terms and .
Simplify each term.
Multiply by .
Multiply by .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify each term.
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Move to the left of .
Rewrite as .
Multiply by .
Expand by multiplying each term in the first expression by each term in the second expression.
Simplify terms.
Simplify each term.
Multiply by by adding the exponents.
Use the power rule to combine exponents.
Multiply by .
Multiply by by adding the exponents.
Move .
Use the power rule to combine exponents.
Multiply by .
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by .
Multiply by .
Simplify by adding terms.
Subtract from .
Divide by .
Factor the left side of the equation.
Regroup terms.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Let . Substitute for all occurrences of .
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Replace all occurrences of with .
Rewrite as .
Factor.
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Remove unnecessary parentheses.
Rewrite as .
Let . Substitute for all occurrences of .
Factor by grouping.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Replace all occurrences of with .
Rewrite as .
Factor.
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Remove unnecessary parentheses.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Apply the distributive property.
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by .
Reorder terms.
Factor.
Rewrite in a factored form.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Remove unnecessary parentheses.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Set the first factor equal to .
Subtract from both sides of the equation.
Set the next factor equal to and solve.
Set the next factor equal to .
Add to both sides of the equation.
Set the next factor equal to and solve.
Set the next factor equal to .
Add to both sides of the equation.
Set the next factor equal to and solve.
Set the next factor equal to .
Subtract from both sides of the equation.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Rewrite as .
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
The final solution is all the values that make true.
Find the Roots (Zeros) 2x^5-2x^4-6x^3+6x^2-8x+8=0

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