y^2-y-5=y-2

Solution for y^2-y-5=y-2 equation:

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

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

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

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

Solving for variable 'y'.

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

Combine like terms: -5 + 2 = -3
-3 + -1y + -1y + y2 = -2 + y + 2 + -1y

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

Reorder the terms:
-3 + -2y + y2 = -2 + 2 + y + -1y

Combine like terms: -2 + 2 = 0
-3 + -2y + y2 = 0 + y + -1y
-3 + -2y + y2 = y + -1y

Combine like terms: y + -1y = 0
-3 + -2y + y2 = 0

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

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

Simplifying
-1 + -1y = 0

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

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

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

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

Simplifying
y = -1
Subproblem 2
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
Solution
y = {-1, 3}