4x-16=12x+8+x^2+3x

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Solution for 4x-16=12x+8+x^2+3x equation: 


Simplifying
4x + -16 = 12x + 8 + x2 + 3x

Reorder the terms:
-16 + 4x = 12x + 8 + x2 + 3x

Reorder the terms:
-16 + 4x = 8 + 12x + 3x + x2

Combine like terms: 12x + 3x = 15x
-16 + 4x = 8 + 15x + x2

Solving
-16 + 4x = 8 + 15x + x2

Solving for variable 'x'.

Reorder the terms:
-16 + -8 + 4x + -15x + -1x2 = 8 + 15x + x2 + -8 + -15x + -1x2

Combine like terms: -16 + -8 = -24
-24 + 4x + -15x + -1x2 = 8 + 15x + x2 + -8 + -15x + -1x2

Combine like terms: 4x + -15x = -11x
-24 + -11x + -1x2 = 8 + 15x + x2 + -8 + -15x + -1x2

Reorder the terms:
-24 + -11x + -1x2 = 8 + -8 + 15x + -15x + x2 + -1x2

Combine like terms: 8 + -8 = 0
-24 + -11x + -1x2 = 0 + 15x + -15x + x2 + -1x2
-24 + -11x + -1x2 = 15x + -15x + x2 + -1x2

Combine like terms: 15x + -15x = 0
-24 + -11x + -1x2 = 0 + x2 + -1x2
-24 + -11x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-24 + -11x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(24 + 11x + x2) = 0

Factor a trinomial.
-1((8 + x)(3 + x)) = 0

Ignore the factor -1.

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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-8, -3}

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