3x^3=3x(x+72)

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Solution for 3x^3=3x(x+72) equation: 


Simplifying
3x3 = 3x(x + 72)

Reorder the terms:
3x3 = 3x(72 + x)
3x3 = (72 * 3x + x * 3x)
3x3 = (216x + 3x2)

Solving
3x3 = 216x + 3x2

Solving for variable 'x'.

Reorder the terms:
-216x + -3x2 + 3x3 = 216x + 3x2 + -216x + -3x2

Reorder the terms:
-216x + -3x2 + 3x3 = 216x + -216x + 3x2 + -3x2

Combine like terms: 216x + -216x = 0
-216x + -3x2 + 3x3 = 0 + 3x2 + -3x2
-216x + -3x2 + 3x3 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-216x + -3x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-72 + -1x + x2) = 0

Factor a trinomial.
3x((-8 + -1x)(9 + -1x)) = 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 '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 3
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {0, -8, 9}

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