5x^3-25x^2=30x

Solution for 5x^3-25x^2=30x equation:

Simplifying
5x3 + -25x2 = 30x

Reorder the terms:
-25x2 + 5x3 = 30x

Solving
-25x2 + 5x3 = 30x

Solving for variable 'x'.

Reorder the terms:
-30x + -25x2 + 5x3 = 30x + -30x

Combine like terms: 30x + -30x = 0
-30x + -25x2 + 5x3 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-6 + -5x + x2) = 0

Factor a trinomial.
5x((-1 + -1x)(6 + -1x)) = 0

Ignore the factor 5.
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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, -1, 6}