y^2-3=y+9

Solution for y^2-3=y+9 equation:

Simplifying
y2 + -3 = y + 9

Reorder the terms:
-3 + y2 = y + 9

Reorder the terms:
-3 + y2 = 9 + y

Solving
-3 + y2 = 9 + y

Solving for variable 'y'.

Reorder the terms:
-3 + -9 + -1y + y2 = 9 + y + -9 + -1y

Combine like terms: -3 + -9 = -12
-12 + -1y + y2 = 9 + y + -9 + -1y

Reorder the terms:
-12 + -1y + y2 = 9 + -9 + y + -1y

Combine like terms: 9 + -9 = 0
-12 + -1y + y2 = 0 + y + -1y
-12 + -1y + y2 = y + -1y

Combine like terms: y + -1y = 0
-12 + -1y + y2 = 0

Factor a trinomial.
(-3 + -1y)(4 + -1y) = 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 '(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 = {-3, 4}