x^3+15x=8x^2

Solution for x^3+15x=8x^2 equation:

Simplifying
x3 + 15x = 8x2

Reorder the terms:
15x + x3 = 8x2

Solving
15x + x3 = 8x2

Solving for variable 'x'.

Reorder the terms:
15x + -8x2 + x3 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
15x + -8x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(15 + -8x + x2) = 0

Factor a trinomial.
x((3 + -1x)(5 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 3, 5}