(2x^2+2)=1+(x-1)(x-1)

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Solution for (2x^2+2)=1+(x-1)(x-1) equation: 


Simplifying
(2x2 + 2) = 1 + (x + -1)(x + -1)

Reorder the terms:
(2 + 2x2) = 1 + (x + -1)(x + -1)

Remove parenthesis around (2 + 2x2)
2 + 2x2 = 1 + (x + -1)(x + -1)

Reorder the terms:
2 + 2x2 = 1 + (-1 + x)(x + -1)

Reorder the terms:
2 + 2x2 = 1 + (-1 + x)(-1 + x)

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

Combine like terms: -1x + -1x = -2x
2 + 2x2 = 1 + (1 + -2x + x2)

Combine like terms: 1 + 1 = 2
2 + 2x2 = 2 + -2x + x2

Add '-2' to each side of the equation.
2 + -2 + 2x2 = 2 + -2x + -2 + x2

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

Reorder the terms:
2x2 = 2 + -2 + -2x + x2

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

Solving
2x2 = -2x + x2

Solving for variable 'x'.

Reorder the terms:
2x + 2x2 + -1x2 = -2x + x2 + 2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
2x + 1x2 = -2x + x2 + 2x + -1x2

Reorder the terms:
2x + 1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
2x + 1x2 = 0 + x2 + -1x2
2x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2x + 1x2 = 0

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {0, -2}

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