100x-x^2-900=0

Solution for 100x-x^2-900=0 equation:

Simplifying
100x + -1x2 + -900 = 0

Reorder the terms:
-900 + 100x + -1x2 = 0

Solving
-900 + 100x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-90 + x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-90 + x)' equal to zero and attempt to solve:

Simplifying
-90 + x = 0

Solving
-90 + x = 0

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

Add '90' to each side of the equation.
-90 + 90 + x = 0 + 90

Combine like terms: -90 + 90 = 0
0 + x = 0 + 90
x = 0 + 90

Combine like terms: 0 + 90 = 90
x = 90

Simplifying
x = 90
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {90, 10}