0=x^3-2x^2-48x

Solution for 0=x^3-2x^2-48x equation:

Simplifying
0 = x3 + -2x2 + -48x

Reorder the terms:
0 = -48x + -2x2 + x3

Solving
0 = -48x + -2x2 + x3

Solving for variable 'x'.
Remove the zero:
48x + 2x2 + -1x3 = -48x + -2x2 + x3 + 48x + 2x2 + -1x3

Reorder the terms:
48x + 2x2 + -1x3 = -48x + 48x + -2x2 + 2x2 + x3 + -1x3

Combine like terms: -48x + 48x = 0
48x + 2x2 + -1x3 = 0 + -2x2 + 2x2 + x3 + -1x3
48x + 2x2 + -1x3 = -2x2 + 2x2 + x3 + -1x3

Combine like terms: -2x2 + 2x2 = 0
48x + 2x2 + -1x3 = 0 + x3 + -1x3
48x + 2x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
48x + 2x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(48 + 2x + -1x2) = 0

Factor a trinomial.
x((8 + -1x)(6 + x)) = 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 '(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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {0, 8, -6}