6y(6+4y)=26

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Solution for 6y(6+4y)=26 equation:


Simplifying
6y(6 + 4y) = 26
(6 * 6y + 4y * 6y) = 26
(36y + 24y2) = 26

Solving
36y + 24y2 = 26

Solving for variable 'y'.

Reorder the terms:
-26 + 36y + 24y2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + 36y + 24y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 18y + 12y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-13 + 18y + 12y2)' equal to zero and attempt to solve:

Simplifying
-13 + 18y + 12y2 = 0

Solving
-13 + 18y + 12y2 = 0

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

Divide each side by '12'.
-1.083333333 + 1.5y + y2 = 0

Move the constant term to the right:

Add '1.083333333' to each side of the equation.
-1.083333333 + 1.5y + 1.083333333 + y2 = 0 + 1.083333333

Reorder the terms:
-1.083333333 + 1.083333333 + 1.5y + y2 = 0 + 1.083333333

Combine like terms: -1.083333333 + 1.083333333 = 0.000000000
0.000000000 + 1.5y + y2 = 0 + 1.083333333
1.5y + y2 = 0 + 1.083333333

Combine like terms: 0 + 1.083333333 = 1.083333333
1.5y + y2 = 1.083333333

The y term is 1.5y.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5y + 0.5625 + y2 = 1.083333333 + 0.5625

Reorder the terms:
0.5625 + 1.5y + y2 = 1.083333333 + 0.5625

Combine like terms: 1.083333333 + 0.5625 = 1.645833333
0.5625 + 1.5y + y2 = 1.645833333

Factor a perfect square on the left side:
(y + 0.75)(y + 0.75) = 1.645833333

Calculate the square root of the right side: 1.28290036

Break this problem into two subproblems by setting 
(y + 0.75) equal to 1.28290036 and -1.28290036.


Subproblem 1
y + 0.75 = 1.28290036

Simplifying
y + 0.75 = 1.28290036

Reorder the terms:
0.75 + y = 1.28290036

Solving
0.75 + y = 1.28290036

Solving for variable 'y'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + y = 1.28290036 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + y = 1.28290036 + -0.75
y = 1.28290036 + -0.75

Combine like terms: 1.28290036 + -0.75 = 0.53290036
y = 0.53290036

Simplifying
y = 0.53290036


Subproblem 2
y + 0.75 = -1.28290036

Simplifying
y + 0.75 = -1.28290036

Reorder the terms:
0.75 + y = -1.28290036

Solving
0.75 + y = -1.28290036

Solving for variable 'y'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + y = -1.28290036 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + y = -1.28290036 + -0.75
y = -1.28290036 + -0.75

Combine like terms: -1.28290036 + -0.75 = -2.03290036
y = -2.03290036

Simplifying
y = -2.03290036


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.53290036, -2.03290036}
Solution
y = {0.53290036, -2.03290036}

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