y^2-8y-11=-5y-1

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Solution for y^2-8y-11=-5y-1 equation: 


Simplifying
y2 + -8y + -11 = -5y + -1

Reorder the terms:
-11 + -8y + y2 = -5y + -1

Reorder the terms:
-11 + -8y + y2 = -1 + -5y

Solving
-11 + -8y + y2 = -1 + -5y

Solving for variable 'y'.

Reorder the terms:
-11 + 1 + -8y + 5y + y2 = -1 + -5y + 1 + 5y

Combine like terms: -11 + 1 = -10
-10 + -8y + 5y + y2 = -1 + -5y + 1 + 5y

Combine like terms: -8y + 5y = -3y
-10 + -3y + y2 = -1 + -5y + 1 + 5y

Reorder the terms:
-10 + -3y + y2 = -1 + 1 + -5y + 5y

Combine like terms: -1 + 1 = 0
-10 + -3y + y2 = 0 + -5y + 5y
-10 + -3y + y2 = -5y + 5y

Combine like terms: -5y + 5y = 0
-10 + -3y + y2 = 0

Factor a trinomial.
(-2 + -1y)(5 + -1y) = 0


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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2

Subproblem 2
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
Solution
y = {-2, 5}

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