3y(y-3)=12

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

Simplifying
3y(y + -3) = 12

Reorder the terms:
3y(-3 + y) = 12
(-3 * 3y + y * 3y) = 12
(-9y + 3y2) = 12

Solving
-9y + 3y2 = 12

Solving for variable 'y'.

Reorder the terms:
-12 + -9y + 3y2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -9y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -3y + y2) = 0

Factor a trinomial.
3((-1 + -1y)(4 + -1y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -1y)' equal to zero and attempt to solve:

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1y = 0 + 1

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

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

Divide each side by '-1'.
y = -1

Simplifying
y = -1
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 = {-1, 4}