4y^2+12y-216=0

Solution for 4y^2+12y-216=0 equation:

Simplifying
4y2 + 12y + -216 = 0

Reorder the terms:
-216 + 12y + 4y2 = 0

Solving
-216 + 12y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-54 + 3y + y2) = 0

Factor a trinomial.
4((-9 + -1y)(6 + -1y)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-9 + -1y)' equal to zero and attempt to solve:

Simplifying
-9 + -1y = 0

Solving
-9 + -1y = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1y = 0 + 9
-1y = 0 + 9

Combine like terms: 0 + 9 = 9
-1y = 9

Divide each side by '-1'.
y = -9

Simplifying
y = -9
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 = {-9, 6}