100y-y^2=2500

Solution for 100y-y^2=2500 equation:

Simplifying
100y + -1y2 = 2500

Solving
100y + -1y2 = 2500

Solving for variable 'y'.

Reorder the terms:
-2500 + 100y + -1y2 = 2500 + -2500

Combine like terms: 2500 + -2500 = 0
-2500 + 100y + -1y2 = 0

Factor a trinomial.
(-50 + y)(50 + -1y) = 0

Subproblem 1
Set the factor '(-50 + y)' equal to zero and attempt to solve:

Simplifying
-50 + y = 0

Solving
-50 + y = 0

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

Add '50' to each side of the equation.
-50 + 50 + y = 0 + 50

Combine like terms: -50 + 50 = 0
0 + y = 0 + 50
y = 0 + 50

Combine like terms: 0 + 50 = 50
y = 50

Simplifying
y = 50
Subproblem 2
Set the factor '(50 + -1y)' equal to zero and attempt to solve:

Simplifying
50 + -1y = 0

Solving
50 + -1y = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1y = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1y = 0 + -50
-1y = 0 + -50

Combine like terms: 0 + -50 = -50
-1y = -50

Divide each side by '-1'.
y = 50

Simplifying
y = 50
Solution
y = {50, 50}