13+4y(116-2y)=232

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Solution for 13+4y(116-2y)=232 equation: 


Simplifying
13 + 4y(116 + -2y) = 232
13 + (116 * 4y + -2y * 4y) = 232
13 + (464y + -8y2) = 232

Solving
13 + 464y + -8y2 = 232

Solving for variable 'y'.

Reorder the terms:
13 + -232 + 464y + -8y2 = 232 + -232

Combine like terms: 13 + -232 = -219
-219 + 464y + -8y2 = 232 + -232

Combine like terms: 232 + -232 = 0
-219 + 464y + -8y2 = 0

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

Divide each side by '-8'.
27.375 + -58y + y2 = 0

Move the constant term to the right:

Add '-27.375' to each side of the equation.
27.375 + -58y + -27.375 + y2 = 0 + -27.375

Reorder the terms:
27.375 + -27.375 + -58y + y2 = 0 + -27.375

Combine like terms: 27.375 + -27.375 = 0.000
0.000 + -58y + y2 = 0 + -27.375
-58y + y2 = 0 + -27.375

Combine like terms: 0 + -27.375 = -27.375
-58y + y2 = -27.375

The y term is -58y.  Take half its coefficient (-29).
Square it (841) and add it to both sides.

Add '841' to each side of the equation.
-58y + 841 + y2 = -27.375 + 841

Reorder the terms:
841 + -58y + y2 = -27.375 + 841

Combine like terms: -27.375 + 841 = 813.625
841 + -58y + y2 = 813.625

Factor a perfect square on the left side:
(y + -29)(y + -29) = 813.625

Calculate the square root of the right side: 28.524112607

Break this problem into two subproblems by setting 
(y + -29) equal to 28.524112607 and -28.524112607.


Subproblem 1
y + -29 = 28.524112607

Simplifying
y + -29 = 28.524112607

Reorder the terms:
-29 + y = 28.524112607

Solving
-29 + y = 28.524112607

Solving for variable 'y'.

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

Add '29' to each side of the equation.
-29 + 29 + y = 28.524112607 + 29

Combine like terms: -29 + 29 = 0
0 + y = 28.524112607 + 29
y = 28.524112607 + 29

Combine like terms: 28.524112607 + 29 = 57.524112607
y = 57.524112607

Simplifying
y = 57.524112607


Subproblem 2
y + -29 = -28.524112607

Simplifying
y + -29 = -28.524112607

Reorder the terms:
-29 + y = -28.524112607

Solving
-29 + y = -28.524112607

Solving for variable 'y'.

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

Add '29' to each side of the equation.
-29 + 29 + y = -28.524112607 + 29

Combine like terms: -29 + 29 = 0
0 + y = -28.524112607 + 29
y = -28.524112607 + 29

Combine like terms: -28.524112607 + 29 = 0.475887393
y = 0.475887393

Simplifying
y = 0.475887393


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {57.524112607, 0.475887393}

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