x=3x^2+12x+8

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


Simplifying
x = 3x2 + 12x + 8

Reorder the terms:
x = 8 + 12x + 3x2

Solving
x = 8 + 12x + 3x2

Solving for variable 'x'.

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

Combine like terms: x + -12x = -11x
-8 + -11x + -3x2 = 8 + 12x + 3x2 + -8 + -12x + -3x2

Reorder the terms:
-8 + -11x + -3x2 = 8 + -8 + 12x + -12x + 3x2 + -3x2

Combine like terms: 8 + -8 = 0
-8 + -11x + -3x2 = 0 + 12x + -12x + 3x2 + -3x2
-8 + -11x + -3x2 = 12x + -12x + 3x2 + -3x2

Combine like terms: 12x + -12x = 0
-8 + -11x + -3x2 = 0 + 3x2 + -3x2
-8 + -11x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-8 + -11x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 11x + 3x2) = 0

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

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 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 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Divide each side by '3'.
x = -2.666666667

Simplifying
x = -2.666666667

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 = {-2.666666667, -1}

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