2x^2-2x+3=-2(x^2-x-1)

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Solution for 2x^2-2x+3=-2(x^2-x-1) equation: 


Simplifying
2x2 + -2x + 3 = -2(x2 + -1x + -1)

Reorder the terms:
3 + -2x + 2x2 = -2(x2 + -1x + -1)

Reorder the terms:
3 + -2x + 2x2 = -2(-1 + -1x + x2)
3 + -2x + 2x2 = (-1 * -2 + -1x * -2 + x2 * -2)
3 + -2x + 2x2 = (2 + 2x + -2x2)

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

Solving for variable 'x'.

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

Combine like terms: 3 + -2 = 1
1 + -2x + -2x + 2x2 + 2x2 = 2 + 2x + -2x2 + -2 + -2x + 2x2

Combine like terms: -2x + -2x = -4x
1 + -4x + 2x2 + 2x2 = 2 + 2x + -2x2 + -2 + -2x + 2x2

Combine like terms: 2x2 + 2x2 = 4x2
1 + -4x + 4x2 = 2 + 2x + -2x2 + -2 + -2x + 2x2

Reorder the terms:
1 + -4x + 4x2 = 2 + -2 + 2x + -2x + -2x2 + 2x2

Combine like terms: 2 + -2 = 0
1 + -4x + 4x2 = 0 + 2x + -2x + -2x2 + 2x2
1 + -4x + 4x2 = 2x + -2x + -2x2 + 2x2

Combine like terms: 2x + -2x = 0
1 + -4x + 4x2 = 0 + -2x2 + 2x2
1 + -4x + 4x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
1 + -4x + 4x2 = 0

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


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0.5, 0.5}

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