12y-36=3y+y(y-3)

Solution for 12y-36=3y+y(y-3) equation:

Simplifying
12y + -36 = 3y + y(y + -3)

Reorder the terms:
-36 + 12y = 3y + y(y + -3)

Reorder the terms:
-36 + 12y = 3y + y(-3 + y)
-36 + 12y = 3y + (-3 * y + y * y)
-36 + 12y = 3y + (-3y + y2)

Combine like terms: 3y + -3y = 0
-36 + 12y = 0 + y2
-36 + 12y = y2

Solving
-36 + 12y = y2

Solving for variable 'y'.

Combine like terms: y2 + -1y2 = 0
-36 + 12y + -1y2 = 0

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

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

Simplifying
-6 + y = 0

Solving
-6 + y = 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 + y = 0 + 6

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

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

Simplifying
y = 6
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 = {6, 6}