12y^2-30y-72=0

Solution for 12y^2-30y-72=0 equation:

Simplifying
12y2 + -30y + -72 = 0

Reorder the terms:
-72 + -30y + 12y2 = 0

Solving
-72 + -30y + 12y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-12 + -5y + 2y2) = 0

Factor a trinomial.
6((-3 + -2y)(4 + -1y)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + -2y)' equal to zero and attempt to solve:

Simplifying
-3 + -2y = 0

Solving
-3 + -2y = 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 + -2y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2y = 0 + 3
-2y = 0 + 3

Combine like terms: 0 + 3 = 3
-2y = 3

Divide each side by '-2'.
y = -1.5

Simplifying
y = -1.5
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 = {-1.5, 4}