-50x=x^3-15x^2

Solution for -50x=x^3-15x^2 equation:

Simplifying
-50x = x3 + -15x2

Reorder the terms:
-50x = -15x2 + x3

Solving
-50x = -15x2 + x3

Solving for variable 'x'.

Reorder the terms:
-50x + 15x2 + -1x3 = -15x2 + 15x2 + x3 + -1x3

Combine like terms: -15x2 + 15x2 = 0
-50x + 15x2 + -1x3 = 0 + x3 + -1x3
-50x + 15x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-50x + 15x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-50 + 15x + -1x2) = 0

Factor a trinomial.
x((-10 + x)(5 + -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 '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 0

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

Add '10' to each side of the equation.
-10 + 10 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Simplifying
x = 10
Subproblem 3
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
Solution
x = {0, 10, 5}