y+12=y(y-3)

Solution for y+12=y(y-3) equation:

Simplifying
y + 12 = y(y + -3)

Reorder the terms:
12 + y = y(y + -3)

Reorder the terms:
12 + y = y(-3 + y)
12 + y = (-3 * y + y * y)
12 + y = (-3y + y2)

Solving
12 + y = -3y + y2

Solving for variable 'y'.

Combine like terms: y + 3y = 4y
12 + 4y + -1y2 = -3y + y2 + 3y + -1y2

Reorder the terms:
12 + 4y + -1y2 = -3y + 3y + y2 + -1y2

Combine like terms: -3y + 3y = 0
12 + 4y + -1y2 = 0 + y2 + -1y2
12 + 4y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
12 + 4y + -1y2 = 0

Factor a trinomial.
(6 + -1y)(2 + y) = 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 '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2
Solution
y = {6, -2}