y^2-12y+24=-y-6

Solution for y^2-12y+24=-y-6 equation:

Simplifying
y2 + -12y + 24 = -1y + -6

Reorder the terms:
24 + -12y + y2 = -1y + -6

Reorder the terms:
24 + -12y + y2 = -6 + -1y

Solving
24 + -12y + y2 = -6 + -1y

Solving for variable 'y'.

Reorder the terms:
24 + 6 + -12y + y + y2 = -6 + -1y + 6 + y

Combine like terms: 24 + 6 = 30
30 + -12y + y + y2 = -6 + -1y + 6 + y

Combine like terms: -12y + y = -11y
30 + -11y + y2 = -6 + -1y + 6 + y

Reorder the terms:
30 + -11y + y2 = -6 + 6 + -1y + y

Combine like terms: -6 + 6 = 0
30 + -11y + y2 = 0 + -1y + y
30 + -11y + y2 = -1y + y

Combine like terms: -1y + y = 0
30 + -11y + y2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
y = {5, 6}