-2y+6=y^2-9

Solution for -2y+6=y^2-9 equation:

Simplifying
-2y + 6 = y2 + -9

Reorder the terms:
6 + -2y = y2 + -9

Reorder the terms:
6 + -2y = -9 + y2

Solving
6 + -2y = -9 + y2

Solving for variable 'y'.

Reorder the terms:
6 + 9 + -2y + -1y2 = -9 + y2 + 9 + -1y2

Combine like terms: 6 + 9 = 15
15 + -2y + -1y2 = -9 + y2 + 9 + -1y2

Reorder the terms:
15 + -2y + -1y2 = -9 + 9 + y2 + -1y2

Combine like terms: -9 + 9 = 0
15 + -2y + -1y2 = 0 + y2 + -1y2
15 + -2y + -1y2 = y2 + -1y2

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

Factor a trinomial.
(3 + -1y)(5 + y) = 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 '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 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 + y = 0 + -5

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

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

Simplifying
y = -5
Solution
y = {3, -5}