x^3=5x^2

Solution for x^3=5x^2 equation:

Simplifying
x3 = 5x2

Solving
x3 = 5x2

Solving for variable 'x'.

Reorder the terms:
-5x2 + x3 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-5x2 + x3 = 0

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

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

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