5y+9=y^2-2y+1

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Solution for 5y+9=y^2-2y+1 equation: 


Simplifying
5y + 9 = y2 + -2y + 1

Reorder the terms:
9 + 5y = y2 + -2y + 1

Reorder the terms:
9 + 5y = 1 + -2y + y2

Solving
9 + 5y = 1 + -2y + y2

Solving for variable 'y'.

Reorder the terms:
9 + -1 + 5y + 2y + -1y2 = 1 + -2y + y2 + -1 + 2y + -1y2

Combine like terms: 9 + -1 = 8
8 + 5y + 2y + -1y2 = 1 + -2y + y2 + -1 + 2y + -1y2

Combine like terms: 5y + 2y = 7y
8 + 7y + -1y2 = 1 + -2y + y2 + -1 + 2y + -1y2

Reorder the terms:
8 + 7y + -1y2 = 1 + -1 + -2y + 2y + y2 + -1y2

Combine like terms: 1 + -1 = 0
8 + 7y + -1y2 = 0 + -2y + 2y + y2 + -1y2
8 + 7y + -1y2 = -2y + 2y + y2 + -1y2

Combine like terms: -2y + 2y = 0
8 + 7y + -1y2 = 0 + y2 + -1y2
8 + 7y + -1y2 = y2 + -1y2

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

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


Subproblem 1
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

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 = {8, -1}

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