10+108y-16y(y)=0

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Solution for 10+108y-16y(y)=0 equation: 


Simplifying
10 + 108y + -16y(y) = 0

Multiply y * y
10 + 108y + -16y2 = 0

Solving
10 + 108y + -16y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 54y + -8y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 54y + -8y2)' equal to zero and attempt to solve:

Simplifying
5 + 54y + -8y2 = 0

Solving
5 + 54y + -8y2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.625 + -6.75y + y2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -6.75y + 0.625 + y2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -6.75y + y2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -6.75y + y2 = 0 + 0.625
-6.75y + y2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-6.75y + y2 = 0.625

The y term is -6.75y.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75y + 11.390625 + y2 = 0.625 + 11.390625

Reorder the terms:
11.390625 + -6.75y + y2 = 0.625 + 11.390625

Combine like terms: 0.625 + 11.390625 = 12.015625
11.390625 + -6.75y + y2 = 12.015625

Factor a perfect square on the left side:
(y + -3.375)(y + -3.375) = 12.015625

Calculate the square root of the right side: 3.466356156

Break this problem into two subproblems by setting 
(y + -3.375) equal to 3.466356156 and -3.466356156.


Subproblem 1
y + -3.375 = 3.466356156

Simplifying
y + -3.375 = 3.466356156

Reorder the terms:
-3.375 + y = 3.466356156

Solving
-3.375 + y = 3.466356156

Solving for variable 'y'.

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

Add '3.375' to each side of the equation.
-3.375 + 3.375 + y = 3.466356156 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
0.000 + y = 3.466356156 + 3.375
y = 3.466356156 + 3.375

Combine like terms: 3.466356156 + 3.375 = 6.841356156
y = 6.841356156

Simplifying
y = 6.841356156


Subproblem 2
y + -3.375 = -3.466356156

Simplifying
y + -3.375 = -3.466356156

Reorder the terms:
-3.375 + y = -3.466356156

Solving
-3.375 + y = -3.466356156

Solving for variable 'y'.

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

Add '3.375' to each side of the equation.
-3.375 + 3.375 + y = -3.466356156 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
0.000 + y = -3.466356156 + 3.375
y = -3.466356156 + 3.375

Combine like terms: -3.466356156 + 3.375 = -0.091356156
y = -0.091356156

Simplifying
y = -0.091356156


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.841356156, -0.091356156}
Solution
y = {6.841356156, -0.091356156}

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