Move to the left side of the equation by subtracting it from both sides.

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Subtract from .

Apply the distributive property.

Simplify.

Multiply by by adding the exponents.

Move .

Multiply by .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Reorder terms.

Factor.

Factor using the rational roots test.

If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.

Find every combination of . These are the possible roots of the polynomial function.

Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.

Substitute into the polynomial.

Raise to the power of .

Multiply by .

Raise to the power of .

Multiply by .

Subtract from .

Multiply by .

Add and .

Subtract from .

Since is a known root, divide the polynomial by to find the quotient polynomial. This polynomial can then be used to find the remaining roots.

Divide by .

Write as a set of factors.

Remove unnecessary parentheses.

Divide each term in by .

Simplify .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Expand by multiplying each term in the first expression by each term in the second expression.

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite using the commutative property of multiplication.

Multiply by by adding the exponents.

Move .

Multiply by .

Move to the left of .

Multiply by .

Multiply by .

Multiply by .

Simplify by adding terms.

Subtract from .

Add and .

Divide by .

If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.

Find every combination of . These are the possible roots of the polynomial function.

Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.

Substitute into the polynomial.

Raise to the power of .

Multiply by .

Raise to the power of .

Multiply by .

Subtract from .

Multiply by .

Add and .

Subtract from .

Since is a known root, divide the polynomial by to find the quotient polynomial. This polynomial can then be used to find the remaining roots.

Divide by .

Write as a set of factors.

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 .

Add to both sides of the equation.

Set the next factor equal to .

Use the quadratic formula to find the solutions.

Substitute the values , , and into the quadratic formula and solve for .

Simplify.

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Multiply by .

Simplify the expression to solve for the portion of the .

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Multiply by .

Change the to .

Simplify the expression to solve for the portion of the .

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Multiply by .

Change the to .

The final answer is the combination of both solutions.

The final solution is all the values that make true.

Find All Complex Solutions (6-2x)(3-2x)x=40