-y^2=2y-3

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

Simplifying
-1y2 = 2y + -3

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

Solving
-1y2 = -3 + 2y

Solving for variable 'y'.

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

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

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

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

Factor a trinomial.
(1 + -1y)(3 + y) = 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 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 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 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

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