6y^2+18y-108=0

Solution for 6y^2+18y-108=0 equation:

Simplifying
6y2 + 18y + -108 = 0

Reorder the terms:
-108 + 18y + 6y2 = 0

Solving
-108 + 18y + 6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-18 + 3y + y2) = 0

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

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

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-6, 3}