(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 + -1x + x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-4, 5}

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