y^2+9y-17=5y-5

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Solution for y^2+9y-17=5y-5 equation: 


Simplifying
y2 + 9y + -17 = 5y + -5

Reorder the terms:
-17 + 9y + y2 = 5y + -5

Reorder the terms:
-17 + 9y + y2 = -5 + 5y

Solving
-17 + 9y + y2 = -5 + 5y

Solving for variable 'y'.

Reorder the terms:
-17 + 5 + 9y + -5y + y2 = -5 + 5y + 5 + -5y

Combine like terms: -17 + 5 = -12
-12 + 9y + -5y + y2 = -5 + 5y + 5 + -5y

Combine like terms: 9y + -5y = 4y
-12 + 4y + y2 = -5 + 5y + 5 + -5y

Reorder the terms:
-12 + 4y + y2 = -5 + 5 + 5y + -5y

Combine like terms: -5 + 5 = 0
-12 + 4y + y2 = 0 + 5y + -5y
-12 + 4y + y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-12 + 4y + y2 = 0

Factor a trinomial.
(-6 + -1y)(2 + -1y) = 0


Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6

Subproblem 2
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
Solution
y = {-6, 2}

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