5y^2+3y-36=0

Solution for 5y^2+3y-36=0 equation:

Simplifying
5y2 + 3y + -36 = 0

Reorder the terms:
-36 + 3y + 5y2 = 0

Solving
-36 + 3y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -1y)(12 + -5y) = 0

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

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 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 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3
Subproblem 2
Set the factor '(12 + -5y)' equal to zero and attempt to solve:

Simplifying
12 + -5y = 0

Solving
12 + -5y = 0

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

Add '-12' to each side of the equation.
12 + -12 + -5y = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -5y = 0 + -12
-5y = 0 + -12

Combine like terms: 0 + -12 = -12
-5y = -12

Divide each side by '-5'.
y = 2.4

Simplifying
y = 2.4
Solution
y = {-3, 2.4}