y^2+34y+120=0

Solution for y^2+34y+120=0 equation:

Simplifying
y2 + 34y + 120 = 0

Reorder the terms:
120 + 34y + y2 = 0

Solving
120 + 34y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(30 + y)(4 + y) = 0

Subproblem 1
Set the factor '(30 + y)' equal to zero and attempt to solve:

Simplifying
30 + y = 0

Solving
30 + y = 0

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

Add '-30' to each side of the equation.
30 + -30 + y = 0 + -30

Combine like terms: 30 + -30 = 0
0 + y = 0 + -30
y = 0 + -30

Combine like terms: 0 + -30 = -30
y = -30

Simplifying
y = -30
Subproblem 2
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 0

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

Add '-4' to each side of the equation.
4 + -4 + y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y = 0 + -4
y = 0 + -4

Combine like terms: 0 + -4 = -4
y = -4

Simplifying
y = -4
Solution
y = {-30, -4}