20x=x^3-x^2

Solution for 20x=x^3-x^2 equation:

Simplifying
20x = x3 + -1x2

Reorder the terms:
20x = -1x2 + x3

Solving
20x = -1x2 + x3

Solving for variable 'x'.

Reorder the terms:
20x + x2 + -1x3 = -1x2 + x2 + x3 + -1x3

Combine like terms: -1x2 + x2 = 0
20x + x2 + -1x3 = 0 + x3 + -1x3
20x + x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
20x + x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(20 + x + -1x2) = 0

Factor a trinomial.
x((5 + -1x)(4 + 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 '(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
Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {0, 5, -4}