2x^2+6x+12=-6x-20+x^2

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Solution for 2x^2+6x+12=-6x-20+x^2 equation: 


Simplifying
2x2 + 6x + 12 = -6x + -20 + x2

Reorder the terms:
12 + 6x + 2x2 = -6x + -20 + x2

Reorder the terms:
12 + 6x + 2x2 = -20 + -6x + x2

Solving
12 + 6x + 2x2 = -20 + -6x + x2

Solving for variable 'x'.

Reorder the terms:
12 + 20 + 6x + 6x + 2x2 + -1x2 = -20 + -6x + x2 + 20 + 6x + -1x2

Combine like terms: 12 + 20 = 32
32 + 6x + 6x + 2x2 + -1x2 = -20 + -6x + x2 + 20 + 6x + -1x2

Combine like terms: 6x + 6x = 12x
32 + 12x + 2x2 + -1x2 = -20 + -6x + x2 + 20 + 6x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
32 + 12x + 1x2 = -20 + -6x + x2 + 20 + 6x + -1x2

Reorder the terms:
32 + 12x + 1x2 = -20 + 20 + -6x + 6x + x2 + -1x2

Combine like terms: -20 + 20 = 0
32 + 12x + 1x2 = 0 + -6x + 6x + x2 + -1x2
32 + 12x + 1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
32 + 12x + 1x2 = 0 + x2 + -1x2
32 + 12x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
32 + 12x + 1x2 = 0

Factor a trinomial.
(8 + x)(4 + x) = 0


Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-8, -4}

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