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

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

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

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

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

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

Solving for variable 'y'.

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

Combine like terms: 2 + 2 = 4
4 + -2y + -3y + y2 = -2 + 3y + 2 + -3y

Combine like terms: -2y + -3y = -5y
4 + -5y + y2 = -2 + 3y + 2 + -3y

Reorder the terms:
4 + -5y + y2 = -2 + 2 + 3y + -3y

Combine like terms: -2 + 2 = 0
4 + -5y + y2 = 0 + 3y + -3y
4 + -5y + y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
4 + -5y + y2 = 0

Factor a trinomial.
(1 + -1y)(4 + -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 '(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 = {1, 4}