3(y^2+8y+15)=0

Solution for 3(y^2+8y+15)=0 equation:

Simplifying
3(y2 + 8y + 15) = 0

Reorder the terms:
3(15 + 8y + y2) = 0
(15 * 3 + 8y * 3 + y2 * 3) = 0
(45 + 24y + 3y2) = 0

Solving
45 + 24y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + 8y + y2) = 0

Factor a trinomial.
3((5 + y)(3 + y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

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

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

Simplifying
y = -5
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
Solution
y = {-5, -3}