0=2x^3+12x^2+16x

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Solution for 0=2x^3+12x^2+16x equation: 


Simplifying
0 = 2x3 + 12x2 + 16x

Reorder the terms:
0 = 16x + 12x2 + 2x3

Solving
0 = 16x + 12x2 + 2x3

Solving for variable 'x'.
Remove the zero:
-16x + -12x2 + -2x3 = 16x + 12x2 + 2x3 + -16x + -12x2 + -2x3

Reorder the terms:
-16x + -12x2 + -2x3 = 16x + -16x + 12x2 + -12x2 + 2x3 + -2x3

Combine like terms: 16x + -16x = 0
-16x + -12x2 + -2x3 = 0 + 12x2 + -12x2 + 2x3 + -2x3
-16x + -12x2 + -2x3 = 12x2 + -12x2 + 2x3 + -2x3

Combine like terms: 12x2 + -12x2 = 0
-16x + -12x2 + -2x3 = 0 + 2x3 + -2x3
-16x + -12x2 + -2x3 = 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
-16x + -12x2 + -2x3 = 0

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(8 + 6x + x2) = 0

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

Ignore the factor -2.

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 '(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

Subproblem 3
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
Solution
x = {0, -4, -2}

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