y(y-2)+y-2=0

Solution for y(y-2)+y-2=0 equation:

Simplifying
y(y + -2) + y + -2 = 0

Reorder the terms:
y(-2 + y) + y + -2 = 0
(-2 * y + y * y) + y + -2 = 0
(-2y + y2) + y + -2 = 0

Reorder the terms:
-2 + -2y + y + y2 = 0

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

Solving
-2 + -1y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -1y)(2 + -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 '(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 = {-1, 2}