x^3=14x^2+32x

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Solution for x^3=14x^2+32x equation: 


Simplifying
x3 = 14x2 + 32x

Reorder the terms:
x3 = 32x + 14x2

Solving
x3 = 32x + 14x2

Solving for variable 'x'.

Reorder the terms:
-32x + -14x2 + x3 = 32x + 14x2 + -32x + -14x2

Reorder the terms:
-32x + -14x2 + x3 = 32x + -32x + 14x2 + -14x2

Combine like terms: 32x + -32x = 0
-32x + -14x2 + x3 = 0 + 14x2 + -14x2
-32x + -14x2 + x3 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
-32x + -14x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-32 + -14x + x2) = 0

Factor a trinomial.
x((-2 + -1x)(16 + -1x)) = 0


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 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 3
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {0, -2, 16}

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