10y^2+12y-144=0

Solution for 10y^2+12y-144=0 equation:

Simplifying
10y2 + 12y + -144 = 0

Reorder the terms:
-144 + 12y + 10y2 = 0

Solving
-144 + 12y + 10y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + 6y + 5y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-72 + 6y + 5y2)' equal to zero and attempt to solve:

Simplifying
-72 + 6y + 5y2 = 0

Solving
-72 + 6y + 5y2 = 0

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

Divide each side by '5'.
-14.4 + 1.2y + y2 = 0

Move the constant term to the right:

Add '14.4' to each side of the equation.
-14.4 + 1.2y + 14.4 + y2 = 0 + 14.4

Reorder the terms:
-14.4 + 14.4 + 1.2y + y2 = 0 + 14.4

Combine like terms: -14.4 + 14.4 = 0.0
0.0 + 1.2y + y2 = 0 + 14.4
1.2y + y2 = 0 + 14.4

Combine like terms: 0 + 14.4 = 14.4
1.2y + y2 = 14.4

The y term is 1.2y.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2y + 0.36 + y2 = 14.4 + 0.36

Reorder the terms:
0.36 + 1.2y + y2 = 14.4 + 0.36

Combine like terms: 14.4 + 0.36 = 14.76
0.36 + 1.2y + y2 = 14.76

Factor a perfect square on the left side:
(y + 0.6)(y + 0.6) = 14.76

Calculate the square root of the right side: 3.841874542

Break this problem into two subproblems by setting 
(y + 0.6) equal to 3.841874542 and -3.841874542.

Subproblem 1
y + 0.6 = 3.841874542

Simplifying
y + 0.6 = 3.841874542

Reorder the terms:
0.6 + y = 3.841874542

Solving
0.6 + y = 3.841874542

Solving for variable 'y'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + y = 3.841874542 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + y = 3.841874542 + -0.6
y = 3.841874542 + -0.6

Combine like terms: 3.841874542 + -0.6 = 3.241874542
y = 3.241874542

Simplifying
y = 3.241874542

Subproblem 2
y + 0.6 = -3.841874542

Simplifying
y + 0.6 = -3.841874542

Reorder the terms:
0.6 + y = -3.841874542

Solving
0.6 + y = -3.841874542

Solving for variable 'y'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + y = -3.841874542 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + y = -3.841874542 + -0.6
y = -3.841874542 + -0.6

Combine like terms: -3.841874542 + -0.6 = -4.441874542
y = -4.441874542

Simplifying
y = -4.441874542

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.241874542, -4.441874542}
Solution
y = {3.241874542, -4.441874542}