12y^2+24y+12=0

Solution for 12y^2+24y+12=0 equation:

Simplifying
12y2 + 24y + 12 = 0

Reorder the terms:
12 + 24y + 12y2 = 0

Solving
12 + 24y + 12y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '12'.
12(1 + 2y + y2) = 0

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

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

Simplifying
1 + y = 0

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

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

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

Simplifying
y = -1
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

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

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

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

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