18x^3=21x^2+72x

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Solution for 18x^3=21x^2+72x equation: 


Simplifying
18x3 = 21x2 + 72x

Reorder the terms:
18x3 = 72x + 21x2

Solving
18x3 = 72x + 21x2

Solving for variable 'x'.

Reorder the terms:
-72x + -21x2 + 18x3 = 72x + 21x2 + -72x + -21x2

Reorder the terms:
-72x + -21x2 + 18x3 = 72x + -72x + 21x2 + -21x2

Combine like terms: 72x + -72x = 0
-72x + -21x2 + 18x3 = 0 + 21x2 + -21x2
-72x + -21x2 + 18x3 = 21x2 + -21x2

Combine like terms: 21x2 + -21x2 = 0
-72x + -21x2 + 18x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-24 + -7x + 6x2) = 0

Factor a trinomial.
3x((-3 + -2x)(8 + -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 '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 3
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
Solution
x = {0, -1.5, 2.666666667}

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