3y^2+51y+90=0

Solution for 3y^2+51y+90=0 equation:

Simplifying
3y2 + 51y + 90 = 0

Reorder the terms:
90 + 51y + 3y2 = 0

Solving
90 + 51y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(30 + 17y + y2) = 0

Factor a trinomial.
3((15 + y)(2 + y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(15 + y)' equal to zero and attempt to solve:

Simplifying
15 + y = 0

Solving
15 + y = 0

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

Add '-15' to each side of the equation.
15 + -15 + y = 0 + -15

Combine like terms: 15 + -15 = 0
0 + y = 0 + -15
y = 0 + -15

Combine like terms: 0 + -15 = -15
y = -15

Simplifying
y = -15
Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2
Solution
y = {-15, -2}