2y^2+15y+32-y^2-12y-36=0

Solution for 2y^2+15y+32-y^2-12y-36=0 equation:

Simplifying
2y2 + 15y + 32 + -1y2 + -12y + -36 = 0

Reorder the terms:
32 + -36 + 15y + -12y + 2y2 + -1y2 = 0

Combine like terms: 32 + -36 = -4
-4 + 15y + -12y + 2y2 + -1y2 = 0

Combine like terms: 15y + -12y = 3y
-4 + 3y + 2y2 + -1y2 = 0

Combine like terms: 2y2 + -1y2 = 1y2
-4 + 3y + 1y2 = 0

Solving
-4 + 3y + 1y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-4 + -1y)(1 + -1y) = 0

Subproblem 1
Set the factor '(-4 + -1y)' equal to zero and attempt to solve:

Simplifying
-4 + -1y = 0

Solving
-4 + -1y = 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 + -1y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1y = 0 + 4
-1y = 0 + 4

Combine like terms: 0 + 4 = 4
-1y = 4

Divide each side by '-1'.
y = -4

Simplifying
y = -4
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1y = 0 + -1

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

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

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

Simplifying
y = 1
Solution
y = {-4, 1}