2y^2+12y-3=0

Solution for 2y^2+12y-3=0 equation:

Simplifying
2y2 + 12y + -3 = 0

Reorder the terms:
-3 + 12y + 2y2 = 0

Solving
-3 + 12y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
-1.5 + 6y + y2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 6y + 1.5 + y2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 6y + y2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 6y + y2 = 0 + 1.5
6y + y2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
6y + y2 = 1.5

The y term is 6y.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6y + 9 + y2 = 1.5 + 9

Reorder the terms:
9 + 6y + y2 = 1.5 + 9

Combine like terms: 1.5 + 9 = 10.5
9 + 6y + y2 = 10.5

Factor a perfect square on the left side:
(y + 3)(y + 3) = 10.5

Calculate the square root of the right side: 3.240370349

Break this problem into two subproblems by setting 
(y + 3) equal to 3.240370349 and -3.240370349.

Subproblem 1
y + 3 = 3.240370349

Simplifying
y + 3 = 3.240370349

Reorder the terms:
3 + y = 3.240370349

Solving
3 + y = 3.240370349

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = 3.240370349 + -3

Combine like terms: 3 + -3 = 0
0 + y = 3.240370349 + -3
y = 3.240370349 + -3

Combine like terms: 3.240370349 + -3 = 0.240370349
y = 0.240370349

Simplifying
y = 0.240370349

Subproblem 2
y + 3 = -3.240370349

Simplifying
y + 3 = -3.240370349

Reorder the terms:
3 + y = -3.240370349

Solving
3 + y = -3.240370349

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = -3.240370349 + -3

Combine like terms: 3 + -3 = 0
0 + y = -3.240370349 + -3
y = -3.240370349 + -3

Combine like terms: -3.240370349 + -3 = -6.240370349
y = -6.240370349

Simplifying
y = -6.240370349

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.240370349, -6.240370349}