2x-2=-2x^2-4x+6

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Solution for 2x-2=-2x^2-4x+6 equation: 


Simplifying
2x + -2 = -2x2 + -4x + 6

Reorder the terms:
-2 + 2x = -2x2 + -4x + 6

Reorder the terms:
-2 + 2x = 6 + -4x + -2x2

Solving
-2 + 2x = 6 + -4x + -2x2

Solving for variable 'x'.

Reorder the terms:
-2 + -6 + 2x + 4x + 2x2 = 6 + -4x + -2x2 + -6 + 4x + 2x2

Combine like terms: -2 + -6 = -8
-8 + 2x + 4x + 2x2 = 6 + -4x + -2x2 + -6 + 4x + 2x2

Combine like terms: 2x + 4x = 6x
-8 + 6x + 2x2 = 6 + -4x + -2x2 + -6 + 4x + 2x2

Reorder the terms:
-8 + 6x + 2x2 = 6 + -6 + -4x + 4x + -2x2 + 2x2

Combine like terms: 6 + -6 = 0
-8 + 6x + 2x2 = 0 + -4x + 4x + -2x2 + 2x2
-8 + 6x + 2x2 = -4x + 4x + -2x2 + 2x2

Combine like terms: -4x + 4x = 0
-8 + 6x + 2x2 = 0 + -2x2 + 2x2
-8 + 6x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-8 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 3x + x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {-4, 1}

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