4y(3y+3)=118

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Solution for 4y(3y+3)=118 equation: 


Simplifying
4y(3y + 3) = 118

Reorder the terms:
4y(3 + 3y) = 118
(3 * 4y + 3y * 4y) = 118
(12y + 12y2) = 118

Solving
12y + 12y2 = 118

Solving for variable 'y'.

Reorder the terms:
-118 + 12y + 12y2 = 118 + -118

Combine like terms: 118 + -118 = 0
-118 + 12y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-59 + 6y + 6y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-59 + 6y + 6y2)' equal to zero and attempt to solve:

Simplifying
-59 + 6y + 6y2 = 0

Solving
-59 + 6y + 6y2 = 0

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

Divide each side by '6'.
-9.833333333 + y + y2 = 0

Move the constant term to the right:

Add '9.833333333' to each side of the equation.
-9.833333333 + y + 9.833333333 + y2 = 0 + 9.833333333

Reorder the terms:
-9.833333333 + 9.833333333 + y + y2 = 0 + 9.833333333

Combine like terms: -9.833333333 + 9.833333333 = 0.000000000
0.000000000 + y + y2 = 0 + 9.833333333
y + y2 = 0 + 9.833333333

Combine like terms: 0 + 9.833333333 = 9.833333333
y + y2 = 9.833333333

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.
 + 0.25 + y2 = 9.833333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + y2 = 9.833333333 + 0.25

Combine like terms: 9.833333333 + 0.25 = 10.083333333
1.25 + y2 = 10.083333333

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 10.083333333

Calculate the square root of the right side: 3.17542648

Break this problem into two subproblems by setting 
(y + 0.5) equal to 3.17542648 and -3.17542648.


Subproblem 1
y + 0.5 = 3.17542648

Simplifying
y + 0.5 = 3.17542648

Reorder the terms:
0.5 + y = 3.17542648

Solving
0.5 + y = 3.17542648

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 = 3.17542648 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 3.17542648 + -0.5
y = 3.17542648 + -0.5

Combine like terms: 3.17542648 + -0.5 = 2.67542648
y = 2.67542648

Simplifying
y = 2.67542648


Subproblem 2
y + 0.5 = -3.17542648

Simplifying
y + 0.5 = -3.17542648

Reorder the terms:
0.5 + y = -3.17542648

Solving
0.5 + y = -3.17542648

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 = -3.17542648 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -3.17542648 + -0.5
y = -3.17542648 + -0.5

Combine like terms: -3.17542648 + -0.5 = -3.67542648
y = -3.67542648

Simplifying
y = -3.67542648


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.67542648, -3.67542648}
Solution
y = {2.67542648, -3.67542648}

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