y^2+4y-17=5y-5

Solution for y^2+4y-17=5y-5 equation:

Simplifying
y2 + 4y + -17 = 5y + -5

Reorder the terms:
-17 + 4y + y2 = 5y + -5

Reorder the terms:
-17 + 4y + y2 = -5 + 5y

Solving
-17 + 4y + y2 = -5 + 5y

Solving for variable 'y'.

Reorder the terms:
-17 + 5 + 4y + -5y + y2 = -5 + 5y + 5 + -5y

Combine like terms: -17 + 5 = -12
-12 + 4y + -5y + y2 = -5 + 5y + 5 + -5y

Combine like terms: 4y + -5y = -1y
-12 + -1y + y2 = -5 + 5y + 5 + -5y

Reorder the terms:
-12 + -1y + y2 = -5 + 5 + 5y + -5y

Combine like terms: -5 + 5 = 0
-12 + -1y + y2 = 0 + 5y + -5y
-12 + -1y + y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-12 + -1y + y2 = 0

Factor a trinomial.
(-3 + -1y)(4 + -1y) = 0

Subproblem 1
Set the factor '(-3 + -1y)' equal to zero and attempt to solve:

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3
Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-3, 4}