(y-8)(y-3)=5y

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Solution for (y-8)(y-3)=5y equation: 


Simplifying
(y + -8)(y + -3) = 5y

Reorder the terms:
(-8 + y)(y + -3) = 5y

Reorder the terms:
(-8 + y)(-3 + y) = 5y

Multiply (-8 + y) * (-3 + y)
(-8(-3 + y) + y(-3 + y)) = 5y
((-3 * -8 + y * -8) + y(-3 + y)) = 5y
((24 + -8y) + y(-3 + y)) = 5y
(24 + -8y + (-3 * y + y * y)) = 5y
(24 + -8y + (-3y + y2)) = 5y

Combine like terms: -8y + -3y = -11y
(24 + -11y + y2) = 5y

Solving
24 + -11y + y2 = 5y

Solving for variable 'y'.

Reorder the terms:
24 + -11y + -5y + y2 = 5y + -5y

Combine like terms: -11y + -5y = -16y
24 + -16y + y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
24 + -16y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -16y + -24 + y2 = 0 + -24

Reorder the terms:
24 + -24 + -16y + y2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -16y + y2 = 0 + -24
-16y + y2 = 0 + -24

Combine like terms: 0 + -24 = -24
-16y + y2 = -24

The y term is -16y.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16y + 64 + y2 = -24 + 64

Reorder the terms:
64 + -16y + y2 = -24 + 64

Combine like terms: -24 + 64 = 40
64 + -16y + y2 = 40

Factor a perfect square on the left side:
(y + -8)(y + -8) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(y + -8) equal to 6.32455532 and -6.32455532.


Subproblem 1
y + -8 = 6.32455532

Simplifying
y + -8 = 6.32455532

Reorder the terms:
-8 + y = 6.32455532

Solving
-8 + y = 6.32455532

Solving for variable 'y'.

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

Add '8' to each side of the equation.
-8 + 8 + y = 6.32455532 + 8

Combine like terms: -8 + 8 = 0
0 + y = 6.32455532 + 8
y = 6.32455532 + 8

Combine like terms: 6.32455532 + 8 = 14.32455532
y = 14.32455532

Simplifying
y = 14.32455532


Subproblem 2
y + -8 = -6.32455532

Simplifying
y + -8 = -6.32455532

Reorder the terms:
-8 + y = -6.32455532

Solving
-8 + y = -6.32455532

Solving for variable 'y'.

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

Add '8' to each side of the equation.
-8 + 8 + y = -6.32455532 + 8

Combine like terms: -8 + 8 = 0
0 + y = -6.32455532 + 8
y = -6.32455532 + 8

Combine like terms: -6.32455532 + 8 = 1.67544468
y = 1.67544468

Simplifying
y = 1.67544468


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {14.32455532, 1.67544468}

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