2(x+1)=-4x+2(x^2-3)

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Solution for 2(x+1)=-4x+2(x^2-3) equation: 


Simplifying
2(x + 1) = -4x + 2(x2 + -3)

Reorder the terms:
2(1 + x) = -4x + 2(x2 + -3)
(1 * 2 + x * 2) = -4x + 2(x2 + -3)
(2 + 2x) = -4x + 2(x2 + -3)

Reorder the terms:
2 + 2x = -4x + 2(-3 + x2)
2 + 2x = -4x + (-3 * 2 + x2 * 2)
2 + 2x = -4x + (-6 + 2x2)

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 + -1x2) = 0

Factor a trinomial.
2((4 + -1x)(1 + x)) = 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 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

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

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