6y(y-11)+8=32

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Solution for 6y(y-11)+8=32 equation: 


Simplifying
6y(y + -11) + 8 = 32

Reorder the terms:
6y(-11 + y) + 8 = 32
(-11 * 6y + y * 6y) + 8 = 32
(-66y + 6y2) + 8 = 32

Reorder the terms:
8 + -66y + 6y2 = 32

Solving
8 + -66y + 6y2 = 32

Solving for variable 'y'.

Reorder the terms:
8 + -32 + -66y + 6y2 = 32 + -32

Combine like terms: 8 + -32 = -24
-24 + -66y + 6y2 = 32 + -32

Combine like terms: 32 + -32 = 0
-24 + -66y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + -11y + y2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-4 + -11y + y2)' equal to zero and attempt to solve:

Simplifying
-4 + -11y + y2 = 0

Solving
-4 + -11y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -11y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + -11y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -11y + y2 = 0 + 4
-11y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
-11y + y2 = 4

The y term is -11y.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11y + 30.25 + y2 = 4 + 30.25

Reorder the terms:
30.25 + -11y + y2 = 4 + 30.25

Combine like terms: 4 + 30.25 = 34.25
30.25 + -11y + y2 = 34.25

Factor a perfect square on the left side:
(y + -5.5)(y + -5.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(y + -5.5) equal to 5.852349955 and -5.852349955.


Subproblem 1
y + -5.5 = 5.852349955

Simplifying
y + -5.5 = 5.852349955

Reorder the terms:
-5.5 + y = 5.852349955

Solving
-5.5 + y = 5.852349955

Solving for variable 'y'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + y = 5.852349955 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + y = 5.852349955 + 5.5
y = 5.852349955 + 5.5

Combine like terms: 5.852349955 + 5.5 = 11.352349955
y = 11.352349955

Simplifying
y = 11.352349955


Subproblem 2
y + -5.5 = -5.852349955

Simplifying
y + -5.5 = -5.852349955

Reorder the terms:
-5.5 + y = -5.852349955

Solving
-5.5 + y = -5.852349955

Solving for variable 'y'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + y = -5.852349955 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + y = -5.852349955 + 5.5
y = -5.852349955 + 5.5

Combine like terms: -5.852349955 + 5.5 = -0.352349955
y = -0.352349955

Simplifying
y = -0.352349955


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.352349955, -0.352349955}
Solution
y = {11.352349955, -0.352349955}

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