3Y^2-36Y=-108

Solution for 3Y^2-36Y=-108 equation:

Simplifying
3Y2 + -36Y = -108

Reorder the terms:
-36Y + 3Y2 = -108

Solving
-36Y + 3Y2 = -108

Solving for variable 'Y'.

Reorder the terms:
108 + -36Y + 3Y2 = -108 + 108

Combine like terms: -108 + 108 = 0
108 + -36Y + 3Y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(36 + -12Y + Y2) = 0

Factor a trinomial.
3((6 + -1Y)(6 + -1Y)) = 0

Ignore the factor 3.
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 '(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}