2(x-1)(x-1)-5=13

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Solution for 2(x-1)(x-1)-5=13 equation: 


Simplifying
2(x + -1)(x + -1) + -5 = 13

Reorder the terms:
2(-1 + x)(x + -1) + -5 = 13

Reorder the terms:
2(-1 + x)(-1 + x) + -5 = 13

Multiply (-1 + x) * (-1 + x)
2(-1(-1 + x) + x(-1 + x)) + -5 = 13
2((-1 * -1 + x * -1) + x(-1 + x)) + -5 = 13
2((1 + -1x) + x(-1 + x)) + -5 = 13
2(1 + -1x + (-1 * x + x * x)) + -5 = 13
2(1 + -1x + (-1x + x2)) + -5 = 13

Combine like terms: -1x + -1x = -2x
2(1 + -2x + x2) + -5 = 13
(1 * 2 + -2x * 2 + x2 * 2) + -5 = 13
(2 + -4x + 2x2) + -5 = 13

Reorder the terms:
2 + -5 + -4x + 2x2 = 13

Combine like terms: 2 + -5 = -3
-3 + -4x + 2x2 = 13

Solving
-3 + -4x + 2x2 = 13

Solving for variable 'x'.

Reorder the terms:
-3 + -13 + -4x + 2x2 = 13 + -13

Combine like terms: -3 + -13 = -16
-16 + -4x + 2x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-16 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -2x + x2) = 0

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

Ignore the factor 2.

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 '(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 = {-2, 4}

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