5y^2+53y+86=0

Solution for 5y^2+53y+86=0 equation:

Simplifying
5y2 + 53y + 86 = 0

Reorder the terms:
86 + 53y + 5y2 = 0

Solving
86 + 53y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(43 + 5y)(2 + y) = 0

Subproblem 1
Set the factor '(43 + 5y)' equal to zero and attempt to solve:

Simplifying
43 + 5y = 0

Solving
43 + 5y = 0

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

Add '-43' to each side of the equation.
43 + -43 + 5y = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 5y = 0 + -43
5y = 0 + -43

Combine like terms: 0 + -43 = -43
5y = -43

Divide each side by '5'.
y = -8.6

Simplifying
y = -8.6
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 = {-8.6, -2}