18x^3=15x^2+12x

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Solution for 18x^3=15x^2+12x equation: 


Simplifying
18x3 = 15x2 + 12x

Reorder the terms:
18x3 = 12x + 15x2

Solving
18x3 = 12x + 15x2

Solving for variable 'x'.

Reorder the terms:
-12x + -15x2 + 18x3 = 12x + 15x2 + -12x + -15x2

Reorder the terms:
-12x + -15x2 + 18x3 = 12x + -12x + 15x2 + -15x2

Combine like terms: 12x + -12x = 0
-12x + -15x2 + 18x3 = 0 + 15x2 + -15x2
-12x + -15x2 + 18x3 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-12x + -15x2 + 18x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-4 + -5x + 6x2) = 0

Factor a trinomial.
3x((-1 + -2x)(4 + -3x)) = 0

Ignore the factor 3.

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 '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

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

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 3
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0, -0.5, 1.333333333}

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