x^3-13x^2=48x

Solution for x^3-13x^2=48x equation:

Simplifying
x3 + -13x2 = 48x

Reorder the terms:
-13x2 + x3 = 48x

Solving
-13x2 + x3 = 48x

Solving for variable 'x'.

Reorder the terms:
-48x + -13x2 + x3 = 48x + -48x

Combine like terms: 48x + -48x = 0
-48x + -13x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-48 + -13x + x2) = 0

Factor a trinomial.
x((-3 + -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 '(-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 '(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, -3, 16}