y^2-8y=40-5y

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Solution for y^2-8y=40-5y equation: 


Simplifying
y2 + -8y = 40 + -5y

Reorder the terms:
-8y + y2 = 40 + -5y

Solving
-8y + y2 = 40 + -5y

Solving for variable 'y'.

Reorder the terms:
-40 + -8y + 5y + y2 = 40 + -5y + -40 + 5y

Combine like terms: -8y + 5y = -3y
-40 + -3y + y2 = 40 + -5y + -40 + 5y

Reorder the terms:
-40 + -3y + y2 = 40 + -40 + -5y + 5y

Combine like terms: 40 + -40 = 0
-40 + -3y + y2 = 0 + -5y + 5y
-40 + -3y + y2 = -5y + 5y

Combine like terms: -5y + 5y = 0
-40 + -3y + y2 = 0

Factor a trinomial.
(-5 + -1y)(8 + -1y) = 0


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

Simplifying
-5 + -1y = 0

Solving
-5 + -1y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1y = 0 + 5
-1y = 0 + 5

Combine like terms: 0 + 5 = 5
-1y = 5

Divide each side by '-1'.
y = -5

Simplifying
y = -5

Subproblem 2
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8
Solution
y = {-5, 8}

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