(x+3)(2x-2)=8x

Solution for (x+3)(2x-2)=8x equation:

Simplifying
(x + 3)(2x + -2) = 8x

Reorder the terms:
(3 + x)(2x + -2) = 8x

Reorder the terms:
(3 + x)(-2 + 2x) = 8x

Multiply (3 + x) * (-2 + 2x)
(3(-2 + 2x) + x(-2 + 2x)) = 8x
((-2 * 3 + 2x * 3) + x(-2 + 2x)) = 8x
((-6 + 6x) + x(-2 + 2x)) = 8x
(-6 + 6x + (-2 * x + 2x * x)) = 8x
(-6 + 6x + (-2x + 2x2)) = 8x

Combine like terms: 6x + -2x = 4x
(-6 + 4x + 2x2) = 8x

Solving
-6 + 4x + 2x2 = 8x

Solving for variable 'x'.

Reorder the terms:
-6 + 4x + -8x + 2x2 = 8x + -8x

Combine like terms: 4x + -8x = -4x
-6 + -4x + 2x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-6 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -2x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1x = 0 + 1
-1x = 0 + 1

Combine like terms: 0 + 1 = 1
-1x = 1

Divide each side by '-1'.
x = -1

Simplifying
x = -1
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1, 3}