10y^2+32y+12=0

Solution for 10y^2+32y+12=0 equation:

Simplifying
10y2 + 32y + 12 = 0

Reorder the terms:
12 + 32y + 10y2 = 0

Solving
12 + 32y + 10y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 16y + 5y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 16y + 5y2)' equal to zero and attempt to solve:

Simplifying
6 + 16y + 5y2 = 0

Solving
6 + 16y + 5y2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
1.2 + 3.2y + y2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 3.2y + -1.2 + y2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 3.2y + y2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 3.2y + y2 = 0 + -1.2
3.2y + y2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
3.2y + y2 = -1.2

The y term is 3.2y.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2y + 2.56 + y2 = -1.2 + 2.56

Reorder the terms:
2.56 + 3.2y + y2 = -1.2 + 2.56

Combine like terms: -1.2 + 2.56 = 1.36
2.56 + 3.2y + y2 = 1.36

Factor a perfect square on the left side:
(y + 1.6)(y + 1.6) = 1.36

Calculate the square root of the right side: 1.166190379

Break this problem into two subproblems by setting 
(y + 1.6) equal to 1.166190379 and -1.166190379.

Subproblem 1
y + 1.6 = 1.166190379

Simplifying
y + 1.6 = 1.166190379

Reorder the terms:
1.6 + y = 1.166190379

Solving
1.6 + y = 1.166190379

Solving for variable 'y'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + y = 1.166190379 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + y = 1.166190379 + -1.6
y = 1.166190379 + -1.6

Combine like terms: 1.166190379 + -1.6 = -0.433809621
y = -0.433809621

Simplifying
y = -0.433809621

Subproblem 2
y + 1.6 = -1.166190379

Simplifying
y + 1.6 = -1.166190379

Reorder the terms:
1.6 + y = -1.166190379

Solving
1.6 + y = -1.166190379

Solving for variable 'y'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + y = -1.166190379 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + y = -1.166190379 + -1.6
y = -1.166190379 + -1.6

Combine like terms: -1.166190379 + -1.6 = -2.766190379
y = -2.766190379

Simplifying
y = -2.766190379

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.433809621, -2.766190379}
Solution
y = {-0.433809621, -2.766190379}