y^2-y-36=-2y-6

Solution for y^2-y-36=-2y-6 equation:

Simplifying
y2 + -1y + -36 = -2y + -6

Reorder the terms:
-36 + -1y + y2 = -2y + -6

Reorder the terms:
-36 + -1y + y2 = -6 + -2y

Solving
-36 + -1y + y2 = -6 + -2y

Solving for variable 'y'.

Reorder the terms:
-36 + 6 + -1y + 2y + y2 = -6 + -2y + 6 + 2y

Combine like terms: -36 + 6 = -30
-30 + -1y + 2y + y2 = -6 + -2y + 6 + 2y

Combine like terms: -1y + 2y = 1y
-30 + 1y + y2 = -6 + -2y + 6 + 2y

Reorder the terms:
-30 + 1y + y2 = -6 + 6 + -2y + 2y

Combine like terms: -6 + 6 = 0
-30 + 1y + y2 = 0 + -2y + 2y
-30 + 1y + y2 = -2y + 2y

Combine like terms: -2y + 2y = 0
-30 + 1y + y2 = 0

Factor a trinomial.
(-6 + -1y)(5 + -1y) = 0

Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6
Subproblem 2
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {-6, 5}