(x+2)(2x-2)=36

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Solution for (x+2)(2x-2)=36 equation: 


Simplifying
(x + 2)(2x + -2) = 36

Reorder the terms:
(2 + x)(2x + -2) = 36

Reorder the terms:
(2 + x)(-2 + 2x) = 36

Multiply (2 + x) * (-2 + 2x)
(2(-2 + 2x) + x(-2 + 2x)) = 36
((-2 * 2 + 2x * 2) + x(-2 + 2x)) = 36
((-4 + 4x) + x(-2 + 2x)) = 36
(-4 + 4x + (-2 * x + 2x * x)) = 36
(-4 + 4x + (-2x + 2x2)) = 36

Combine like terms: 4x + -2x = 2x
(-4 + 2x + 2x2) = 36

Solving
-4 + 2x + 2x2 = 36

Solving for variable 'x'.

Reorder the terms:
-4 + -36 + 2x + 2x2 = 36 + -36

Combine like terms: -4 + -36 = -40
-40 + 2x + 2x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-40 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + x + x2) = 0

Factor a trinomial.
2((-5 + -1x)(4 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-5, 4}

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