(y^2)(6y+36)=0

Solution for (y^2)(6y+36)=0 equation:

Simplifying
(y2)(6y + 36) = 0

Reorder the terms:
y2(36 + 6y) = 0
(36 * y2 + 6y * y2) = 0
(36y2 + 6y3) = 0

Solving
36y2 + 6y3 = 0

Solving for variable 'y'.

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

Ignore the factor 6.
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}