(2x-2)*(2x-2)=46+2x^2

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Solution for (2x-2)*(2x-2)=46+2x^2 equation: 


Simplifying
(2x + -2)(2x + -2) = 46 + 2x2

Reorder the terms:
(-2 + 2x)(2x + -2) = 46 + 2x2

Reorder the terms:
(-2 + 2x)(-2 + 2x) = 46 + 2x2

Multiply (-2 + 2x) * (-2 + 2x)
(-2(-2 + 2x) + 2x * (-2 + 2x)) = 46 + 2x2
((-2 * -2 + 2x * -2) + 2x * (-2 + 2x)) = 46 + 2x2
((4 + -4x) + 2x * (-2 + 2x)) = 46 + 2x2
(4 + -4x + (-2 * 2x + 2x * 2x)) = 46 + 2x2
(4 + -4x + (-4x + 4x2)) = 46 + 2x2

Combine like terms: -4x + -4x = -8x
(4 + -8x + 4x2) = 46 + 2x2

Solving
4 + -8x + 4x2 = 46 + 2x2

Solving for variable 'x'.

Reorder the terms:
4 + -46 + -8x + 4x2 + -2x2 = 46 + 2x2 + -46 + -2x2

Combine like terms: 4 + -46 = -42
-42 + -8x + 4x2 + -2x2 = 46 + 2x2 + -46 + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
-42 + -8x + 2x2 = 46 + 2x2 + -46 + -2x2

Reorder the terms:
-42 + -8x + 2x2 = 46 + -46 + 2x2 + -2x2

Combine like terms: 46 + -46 = 0
-42 + -8x + 2x2 = 0 + 2x2 + -2x2
-42 + -8x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-42 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -4x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(7 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-3, 7}

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