y^3=6y^2

Solution for y^3=6y^2 equation:

Simplifying
y3 = 6y2

Solving
y3 = 6y2

Solving for variable 'y'.

Reorder the terms:
-6y2 + y3 = 6y2 + -6y2

Combine like terms: 6y2 + -6y2 = 0
-6y2 + y3 = 0

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(-6 + y) = 0

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}
Subproblem 2
Set the factor '(-6 + y)' equal to zero and attempt to solve:

Simplifying
-6 + y = 0

Solving
-6 + y = 0

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

Add '6' to each side of the equation.
-6 + 6 + y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + y = 0 + 6
y = 0 + 6

Combine like terms: 0 + 6 = 6
y = 6

Simplifying
y = 6
Solution
y = {0, 6}