15y^2+48y+6=

Solution for 15y^2+48y+6= equation:

Simplifying
15y2 + 48y + 6 = 0

Reorder the terms:
6 + 48y + 15y2 = 0

Solving
6 + 48y + 15y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 16y + 5y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + 16y + 5y2)' equal to zero and attempt to solve:

Simplifying
2 + 16y + 5y2 = 0

Solving
2 + 16y + 5y2 = 0

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

Divide each side by '5'.
0.4 + 3.2y + y2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 3.2y + -0.4 + y2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 3.2y + y2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 3.2y + y2 = 0 + -0.4
3.2y + y2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
3.2y + y2 = -0.4

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 = -0.4 + 2.56

Reorder the terms:
2.56 + 3.2y + y2 = -0.4 + 2.56

Combine like terms: -0.4 + 2.56 = 2.16
2.56 + 3.2y + y2 = 2.16

Factor a perfect square on the left side:
(y + 1.6)(y + 1.6) = 2.16

Calculate the square root of the right side: 1.469693846

Break this problem into two subproblems by setting 
(y + 1.6) equal to 1.469693846 and -1.469693846.

Subproblem 1
y + 1.6 = 1.469693846

Simplifying
y + 1.6 = 1.469693846

Reorder the terms:
1.6 + y = 1.469693846

Solving
1.6 + y = 1.469693846

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 = 1.469693846 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + y = 1.469693846 + -1.6
y = 1.469693846 + -1.6

Combine like terms: 1.469693846 + -1.6 = -0.130306154
y = -0.130306154

Simplifying
y = -0.130306154

Subproblem 2
y + 1.6 = -1.469693846

Simplifying
y + 1.6 = -1.469693846

Reorder the terms:
1.6 + y = -1.469693846

Solving
1.6 + y = -1.469693846

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 = -1.469693846 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + y = -1.469693846 + -1.6
y = -1.469693846 + -1.6

Combine like terms: -1.469693846 + -1.6 = -3.069693846
y = -3.069693846

Simplifying
y = -3.069693846

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.130306154, -3.069693846}
Solution
y = {-0.130306154, -3.069693846}