2y-y^2=4y-5y

Solution for 2y-y^2=4y-5y equation:

Simplifying
2y + -1y2 = 4y + -5y

Combine like terms: 4y + -5y = -1y
2y + -1y2 = -1y

Solving
2y + -1y2 = -1y

Solving for variable 'y'.

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

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

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

Factor out the Greatest Common Factor (GCF), 'y'.
y(3 + -1y) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

Move all terms containing y to the left, all other terms to the right.

Simplifying
y = 0
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 = {0, 3}