(100-x)-9x(x-100)=0

Solution for (100-x)-9x(x-100)=0 equation:

Simplifying
(100 + -1x) + -9x(x + -100) = 0

Remove parenthesis around (100 + -1x)
100 + -1x + -9x(x + -100) = 0

Reorder the terms:
100 + -1x + -9x(-100 + x) = 0
100 + -1x + (-100 * -9x + x * -9x) = 0
100 + -1x + (900x + -9x2) = 0

Combine like terms: -1x + 900x = 899x
100 + 899x + -9x2 = 0

Solving
100 + 899x + -9x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(100 + -1x)(1 + 9x) = 0

Subproblem 1
Set the factor '(100 + -1x)' equal to zero and attempt to solve:

Simplifying
100 + -1x = 0

Solving
100 + -1x = 0

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

Add '-100' to each side of the equation.
100 + -100 + -1x = 0 + -100

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

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

Divide each side by '-1'.
x = 100

Simplifying
x = 100
Subproblem 2
Set the factor '(1 + 9x)' equal to zero and attempt to solve:

Simplifying
1 + 9x = 0

Solving
1 + 9x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 9x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9x = 0 + -1
9x = 0 + -1

Combine like terms: 0 + -1 = -1
9x = -1

Divide each side by '9'.
x = -0.1111111111

Simplifying
x = -0.1111111111
Solution
x = {100, -0.1111111111}