y^2-2y-17=-3y+3

Solution for y^2-2y-17=-3y+3 equation:

Simplifying
y2 + -2y + -17 = -3y + 3

Reorder the terms:
-17 + -2y + y2 = -3y + 3

Reorder the terms:
-17 + -2y + y2 = 3 + -3y

Solving
-17 + -2y + y2 = 3 + -3y

Solving for variable 'y'.

Reorder the terms:
-17 + -3 + -2y + 3y + y2 = 3 + -3y + -3 + 3y

Combine like terms: -17 + -3 = -20
-20 + -2y + 3y + y2 = 3 + -3y + -3 + 3y

Combine like terms: -2y + 3y = 1y
-20 + 1y + y2 = 3 + -3y + -3 + 3y

Reorder the terms:
-20 + 1y + y2 = 3 + -3 + -3y + 3y

Combine like terms: 3 + -3 = 0
-20 + 1y + y2 = 0 + -3y + 3y
-20 + 1y + y2 = -3y + 3y

Combine like terms: -3y + 3y = 0
-20 + 1y + y2 = 0

Factor a trinomial.
(-5 + -1y)(4 + -1y) = 0

Subproblem 1
Set the factor '(-5 + -1y)' equal to zero and attempt to solve:

Simplifying
-5 + -1y = 0

Solving
-5 + -1y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1y = 0 + 5

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

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

Divide each side by '-1'.
y = -5

Simplifying
y = -5
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 = {-5, 4}