0=4x^3+12x^2+8x

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Solution for 0=4x^3+12x^2+8x equation: 


Simplifying
0 = 4x3 + 12x2 + 8x

Reorder the terms:
0 = 8x + 12x2 + 4x3

Solving
0 = 8x + 12x2 + 4x3

Solving for variable 'x'.
Remove the zero:
-8x + -12x2 + -4x3 = 8x + 12x2 + 4x3 + -8x + -12x2 + -4x3

Reorder the terms:
-8x + -12x2 + -4x3 = 8x + -8x + 12x2 + -12x2 + 4x3 + -4x3

Combine like terms: 8x + -8x = 0
-8x + -12x2 + -4x3 = 0 + 12x2 + -12x2 + 4x3 + -4x3
-8x + -12x2 + -4x3 = 12x2 + -12x2 + 4x3 + -4x3

Combine like terms: 12x2 + -12x2 = 0
-8x + -12x2 + -4x3 = 0 + 4x3 + -4x3
-8x + -12x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-8x + -12x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), '-4x'.
-4x(2 + 3x + x2) = 0

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

Ignore the factor -4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

Subproblem 3
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 = {0, -2, -1}

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