y^2+3y=36-2y

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

Simplifying
y2 + 3y = 36 + -2y

Reorder the terms:
3y + y2 = 36 + -2y

Solving
3y + y2 = 36 + -2y

Solving for variable 'y'.

Reorder the terms:
-36 + 3y + 2y + y2 = 36 + -2y + -36 + 2y

Combine like terms: 3y + 2y = 5y
-36 + 5y + y2 = 36 + -2y + -36 + 2y

Reorder the terms:
-36 + 5y + y2 = 36 + -36 + -2y + 2y

Combine like terms: 36 + -36 = 0
-36 + 5y + y2 = 0 + -2y + 2y
-36 + 5y + y2 = -2y + 2y

Combine like terms: -2y + 2y = 0
-36 + 5y + y2 = 0

Factor a trinomial.
(-9 + -1y)(4 + -1y) = 0

Subproblem 1
Set the factor '(-9 + -1y)' equal to zero and attempt to solve:

Simplifying
-9 + -1y = 0

Solving
-9 + -1y = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1y = 0 + 9
-1y = 0 + 9

Combine like terms: 0 + 9 = 9
-1y = 9

Divide each side by '-1'.
y = -9

Simplifying
y = -9
Subproblem 2
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
Solution
y = {-9, 4}