2y^2+55y+102=0

Solution for 2y^2+55y+102=0 equation:

Simplifying
2y2 + 55y + 102 = 0

Reorder the terms:
102 + 55y + 2y2 = 0

Solving
102 + 55y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(51 + 2y)(2 + y) = 0

Subproblem 1
Set the factor '(51 + 2y)' equal to zero and attempt to solve:

Simplifying
51 + 2y = 0

Solving
51 + 2y = 0

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

Add '-51' to each side of the equation.
51 + -51 + 2y = 0 + -51

Combine like terms: 51 + -51 = 0
0 + 2y = 0 + -51
2y = 0 + -51

Combine like terms: 0 + -51 = -51
2y = -51

Divide each side by '2'.
y = -25.5

Simplifying
y = -25.5
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 = {-25.5, -2}