2(2x+1)-2(2x-1)=2(x+6)-x^2

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Solution for 2(2x+1)-2(2x-1)=2(x+6)-x^2 equation: 


Simplifying
2(2x + 1) + -2(2x + -1) = 2(x + 6) + -1x2

Reorder the terms:
2(1 + 2x) + -2(2x + -1) = 2(x + 6) + -1x2
(1 * 2 + 2x * 2) + -2(2x + -1) = 2(x + 6) + -1x2
(2 + 4x) + -2(2x + -1) = 2(x + 6) + -1x2

Reorder the terms:
2 + 4x + -2(-1 + 2x) = 2(x + 6) + -1x2
2 + 4x + (-1 * -2 + 2x * -2) = 2(x + 6) + -1x2
2 + 4x + (2 + -4x) = 2(x + 6) + -1x2

Reorder the terms:
2 + 2 + 4x + -4x = 2(x + 6) + -1x2

Combine like terms: 2 + 2 = 4
4 + 4x + -4x = 2(x + 6) + -1x2

Combine like terms: 4x + -4x = 0
4 + 0 = 2(x + 6) + -1x2
4 = 2(x + 6) + -1x2

Reorder the terms:
4 = 2(6 + x) + -1x2
4 = (6 * 2 + x * 2) + -1x2
4 = (12 + 2x) + -1x2

Solving
4 = 12 + 2x + -1x2

Solving for variable 'x'.

Combine like terms: 4 + -12 = -8
-8 + -2x + x2 = 12 + 2x + -1x2 + -12 + -2x + x2

Reorder the terms:
-8 + -2x + x2 = 12 + -12 + 2x + -2x + -1x2 + x2

Combine like terms: 12 + -12 = 0
-8 + -2x + x2 = 0 + 2x + -2x + -1x2 + x2
-8 + -2x + x2 = 2x + -2x + -1x2 + x2

Combine like terms: 2x + -2x = 0
-8 + -2x + x2 = 0 + -1x2 + x2
-8 + -2x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-8 + -2x + x2 = 0

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


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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