3y=12y^2-144

Solution for 3y=12y^2-144 equation:

Simplifying
3y = 12y2 + -144

Reorder the terms:
3y = -144 + 12y2

Solving
3y = -144 + 12y2

Solving for variable 'y'.

Reorder the terms:
144 + 3y + -12y2 = -144 + 12y2 + 144 + -12y2

Reorder the terms:
144 + 3y + -12y2 = -144 + 144 + 12y2 + -12y2

Combine like terms: -144 + 144 = 0
144 + 3y + -12y2 = 0 + 12y2 + -12y2
144 + 3y + -12y2 = 12y2 + -12y2

Combine like terms: 12y2 + -12y2 = 0
144 + 3y + -12y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(48 + y + -4y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(48 + y + -4y2)' equal to zero and attempt to solve:

Simplifying
48 + y + -4y2 = 0

Solving
48 + y + -4y2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-12 + -0.25y + y2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -0.25y + 12 + y2 = 0 + 12

Reorder the terms:
-12 + 12 + -0.25y + y2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -0.25y + y2 = 0 + 12
-0.25y + y2 = 0 + 12

Combine like terms: 0 + 12 = 12
-0.25y + y2 = 12

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.25y + 0.25 + y2 = 12 + 0.25

Reorder the terms:
0.25 + -0.25y + y2 = 12 + 0.25

Combine like terms: 12 + 0.25 = 12.25
0.25 + -0.25y + y2 = 12.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 12.25

Calculate the square root of the right side: 3.5

Break this problem into two subproblems by setting 
(y + 0.5) equal to 3.5 and -3.5.

Subproblem 1
y + 0.5 = 3.5

Simplifying
y + 0.5 = 3.5

Reorder the terms:
0.5 + y = 3.5

Solving
0.5 + y = 3.5

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 3.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 3.5 + -0.5
y = 3.5 + -0.5

Combine like terms: 3.5 + -0.5 = 3
y = 3

Simplifying
y = 3

Subproblem 2
y + 0.5 = -3.5

Simplifying
y + 0.5 = -3.5

Reorder the terms:
0.5 + y = -3.5

Solving
0.5 + y = -3.5

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -3.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -3.5 + -0.5
y = -3.5 + -0.5

Combine like terms: -3.5 + -0.5 = -4
y = -4

Simplifying
y = -4

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3, -4}
Solution
y = {3, -4}