x(100-x)=2500

Solution for x(100-x)=2500 equation:

Simplifying
x(100 + -1x) = 2500
(100 * x + -1x * x) = 2500
(100x + -1x2) = 2500

Solving
100x + -1x2 = 2500

Solving for variable 'x'.

Reorder the terms:
-2500 + 100x + -1x2 = 2500 + -2500

Combine like terms: 2500 + -2500 = 0
-2500 + 100x + -1x2 = 0

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

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

Simplifying
-50 + x = 0

Solving
-50 + x = 0

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

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

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

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

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

Simplifying
50 + -1x = 0

Solving
50 + -1x = 0

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

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

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

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

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

Simplifying
x = 50
Solution
x = {50, 50}