(x-2)(x-2)-36=0

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Solution for (x-2)(x-2)-36=0 equation: 


Simplifying
(x + -2)(x + -2) + -36 = 0

Reorder the terms:
(-2 + x)(x + -2) + -36 = 0

Reorder the terms:
(-2 + x)(-2 + x) + -36 = 0

Multiply (-2 + x) * (-2 + x)
(-2(-2 + x) + x(-2 + x)) + -36 = 0
((-2 * -2 + x * -2) + x(-2 + x)) + -36 = 0
((4 + -2x) + x(-2 + x)) + -36 = 0
(4 + -2x + (-2 * x + x * x)) + -36 = 0
(4 + -2x + (-2x + x2)) + -36 = 0

Combine like terms: -2x + -2x = -4x
(4 + -4x + x2) + -36 = 0

Reorder the terms:
4 + -36 + -4x + x2 = 0

Combine like terms: 4 + -36 = -32
-32 + -4x + x2 = 0

Solving
-32 + -4x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -1x)(8 + -1x) = 0


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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-4, 8}

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