6y^2-66y-72=0

Solution for 6y^2-66y-72=0 equation:

Simplifying
6y2 + -66y + -72 = 0

Reorder the terms:
-72 + -66y + 6y2 = 0

Solving
-72 + -66y + 6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-12 + -11y + y2) = 0

Factor a trinomial.
6((-1 + -1y)(12 + -1y)) = 0

Ignore the factor 6.
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 '(12 + -1y)' equal to zero and attempt to solve:

Simplifying
12 + -1y = 0

Solving
12 + -1y = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1y = 0 + -12

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

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

Divide each side by '-1'.
y = 12

Simplifying
y = 12
Solution
y = {-1, 12}