(2x-6)*(2x-6)=100

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Solution for (2x-6)*(2x-6)=100 equation: 


Simplifying
(2x + -6)(2x + -6) = 100

Reorder the terms:
(-6 + 2x)(2x + -6) = 100

Reorder the terms:
(-6 + 2x)(-6 + 2x) = 100

Multiply (-6 + 2x) * (-6 + 2x)
(-6(-6 + 2x) + 2x * (-6 + 2x)) = 100
((-6 * -6 + 2x * -6) + 2x * (-6 + 2x)) = 100
((36 + -12x) + 2x * (-6 + 2x)) = 100
(36 + -12x + (-6 * 2x + 2x * 2x)) = 100
(36 + -12x + (-12x + 4x2)) = 100

Combine like terms: -12x + -12x = -24x
(36 + -24x + 4x2) = 100

Solving
36 + -24x + 4x2 = 100

Solving for variable 'x'.

Reorder the terms:
36 + -100 + -24x + 4x2 = 100 + -100

Combine like terms: 36 + -100 = -64
-64 + -24x + 4x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-64 + -24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + -6x + x2) = 0

Factor a trinomial.
4((-2 + -1x)(8 + -1x)) = 0

Ignore the factor 4.

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 '(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 = {-2, 8}

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