100=25x-x^2

Solution for 100=25x-x^2 equation:

Simplifying
100 = 25x + -1x2

Solving
100 = 25x + -1x2

Solving for variable 'x'.

Reorder the terms:
100 + -25x + x2 = 25x + -25x + -1x2 + x2

Combine like terms: 25x + -25x = 0
100 + -25x + x2 = 0 + -1x2 + x2
100 + -25x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
100 + -25x + x2 = 0

Factor a trinomial.
(5 + -1x)(20 + -1x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {5, 20}