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((-6 + -1x)(1 + -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 '(-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
Subproblem 3
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
Solution
x = {0, -6, 1}