6y^2+12y+9=27

Solution for 6y^2+12y+9=27 equation:

Simplifying
6y2 + 12y + 9 = 27

Reorder the terms:
9 + 12y + 6y2 = 27

Solving
9 + 12y + 6y2 = 27

Solving for variable 'y'.

Reorder the terms:
9 + -27 + 12y + 6y2 = 27 + -27

Combine like terms: 9 + -27 = -18
-18 + 12y + 6y2 = 27 + -27

Combine like terms: 27 + -27 = 0
-18 + 12y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + 2y + y2) = 0

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

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
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
Solution
y = {-3, 1}