(x-2)(x-2)-16=0

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Solution for (x-2)(x-2)-16=0 equation: 


Simplifying
(x + -2)(x + -2) + -16 = 0

Reorder the terms:
(-2 + x)(x + -2) + -16 = 0

Reorder the terms:
(-2 + x)(-2 + x) + -16 = 0

Multiply (-2 + x) * (-2 + x)
(-2(-2 + x) + x(-2 + x)) + -16 = 0
((-2 * -2 + x * -2) + x(-2 + x)) + -16 = 0
((4 + -2x) + x(-2 + x)) + -16 = 0
(4 + -2x + (-2 * x + x * x)) + -16 = 0
(4 + -2x + (-2x + x2)) + -16 = 0

Combine like terms: -2x + -2x = -4x
(4 + -4x + x2) + -16 = 0

Reorder the terms:
4 + -16 + -4x + x2 = 0

Combine like terms: 4 + -16 = -12
-12 + -4x + x2 = 0

Solving
-12 + -4x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -1x)(6 + -1x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-2, 6}

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