2y^2-5y+3-y^2+2y-1=0

Solution for 2y^2-5y+3-y^2+2y-1=0 equation:

Simplifying
2y2 + -5y + 3 + -1y2 + 2y + -1 = 0

Reorder the terms:
3 + -1 + -5y + 2y + 2y2 + -1y2 = 0

Combine like terms: 3 + -1 = 2
2 + -5y + 2y + 2y2 + -1y2 = 0

Combine like terms: -5y + 2y = -3y
2 + -3y + 2y2 + -1y2 = 0

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

Solving
2 + -3y + 1y2 = 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}