x^3-20x=-x^2

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

Simplifying
x3 + -20x = -1x2

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

Solving
-20x + x3 = -1x2

Solving for variable 'x'.

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

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

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

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

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