(y-8)(y+2)=y-8

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Solution for (y-8)(y+2)=y-8 equation: 


Simplifying
(y + -8)(y + 2) = y + -8

Reorder the terms:
(-8 + y)(y + 2) = y + -8

Reorder the terms:
(-8 + y)(2 + y) = y + -8

Multiply (-8 + y) * (2 + y)
(-8(2 + y) + y(2 + y)) = y + -8
((2 * -8 + y * -8) + y(2 + y)) = y + -8
((-16 + -8y) + y(2 + y)) = y + -8
(-16 + -8y + (2 * y + y * y)) = y + -8
(-16 + -8y + (2y + y2)) = y + -8

Combine like terms: -8y + 2y = -6y
(-16 + -6y + y2) = y + -8

Reorder the terms:
-16 + -6y + y2 = -8 + y

Solving
-16 + -6y + y2 = -8 + y

Solving for variable 'y'.

Reorder the terms:
-16 + 8 + -6y + -1y + y2 = -8 + y + 8 + -1y

Combine like terms: -16 + 8 = -8
-8 + -6y + -1y + y2 = -8 + y + 8 + -1y

Combine like terms: -6y + -1y = -7y
-8 + -7y + y2 = -8 + y + 8 + -1y

Reorder the terms:
-8 + -7y + y2 = -8 + 8 + y + -1y

Combine like terms: -8 + 8 = 0
-8 + -7y + y2 = 0 + y + -1y
-8 + -7y + y2 = y + -1y

Combine like terms: y + -1y = 0
-8 + -7y + y2 = 0

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


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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

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

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

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

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

Simplifying
y = -1

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 = {-1, 8}

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