-y^2+8y+12=-y+2

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Solution for -y^2+8y+12=-y+2 equation: 


Simplifying
-1y2 + 8y + 12 = -1y + 2

Reorder the terms:
12 + 8y + -1y2 = -1y + 2

Reorder the terms:
12 + 8y + -1y2 = 2 + -1y

Solving
12 + 8y + -1y2 = 2 + -1y

Solving for variable 'y'.

Reorder the terms:
12 + -2 + 8y + y + -1y2 = 2 + -1y + -2 + y

Combine like terms: 12 + -2 = 10
10 + 8y + y + -1y2 = 2 + -1y + -2 + y

Combine like terms: 8y + y = 9y
10 + 9y + -1y2 = 2 + -1y + -2 + y

Reorder the terms:
10 + 9y + -1y2 = 2 + -2 + -1y + y

Combine like terms: 2 + -2 = 0
10 + 9y + -1y2 = 0 + -1y + y
10 + 9y + -1y2 = -1y + y

Combine like terms: -1y + y = 0
10 + 9y + -1y2 = 0

Factor a trinomial.
(10 + -1y)(1 + y) = 0


Subproblem 1
Set the factor '(10 + -1y)' equal to zero and attempt to solve:

Simplifying
10 + -1y = 0

Solving
10 + -1y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1y = 0 + -10
-1y = 0 + -10

Combine like terms: 0 + -10 = -10
-1y = -10

Divide each side by '-1'.
y = 10

Simplifying
y = 10

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

Simplifying
1 + y = 0

Solving
1 + y = 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 + y = 0 + -1

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

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

Simplifying
y = -1
Solution
y = {10, -1}

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