# Find the Roots (Zeros) x^4+x^2=4x^3-12x+12

Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
Add to both sides of the equation.
Move to the left side of the equation by subtracting it from both sides.
Factor the left side of the equation.
Regroup terms.
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 .
Factor out of .
Factor out of .
Factor out of .
Let . Substitute for all occurrences of .
Factor using the perfect square rule.
Rearrange terms.
Rewrite as .
Check the middle term by multiplying and compare this result with the middle term in the original expression.
Simplify.
Factor using the perfect square trinomial rule , where and .
Replace all occurrences of with .
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 .
Add to 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.
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.
Set the next factor equal to and solve.
Set the next factor equal to .
Set the equal to .
Add to both sides of the equation.
The final solution is all the values that make true.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Find the Roots (Zeros) x^4+x^2=4x^3-12x+12