x^3-20x^2=21x

Solution for x^3-20x^2=21x equation:

Simplifying
x3 + -20x2 = 21x

Reorder the terms:
-20x2 + x3 = 21x

Solving
-20x2 + x3 = 21x

Solving for variable 'x'.

Reorder the terms:
-21x + -20x2 + x3 = 21x + -21x

Combine like terms: 21x + -21x = 0
-21x + -20x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-21 + -20x + x2) = 0

Factor a trinomial.
x((-1 + -1x)(21 + -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 '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 3
Set the factor '(21 + -1x)' equal to zero and attempt to solve:

Simplifying
21 + -1x = 0

Solving
21 + -1x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x = 0 + -21
-1x = 0 + -21

Combine like terms: 0 + -21 = -21
-1x = -21

Divide each side by '-1'.
x = 21

Simplifying
x = 21
Solution
x = {0, -1, 21}