6y^2(y^2+6y+9)=

Solution for 6y^2(y^2+6y+9)= equation:

Simplifying
6y2(y2 + 6y + 9) = 0

Reorder the terms:
6y2(9 + 6y + y2) = 0
(9 * 6y2 + 6y * 6y2 + y2 * 6y2) = 0
(54y2 + 36y3 + 6y4) = 0

Solving
54y2 + 36y3 + 6y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6y2'.
6y2(9 + 6y + y2) = 0

Factor a trinomial.
6y2((3 + y)(3 + 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 '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Subproblem 3
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Solution
y = {0, -3, -3}