x(x-1)=100-x

Solution for x(x-1)=100-x equation:

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

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

Add 'x' to each side of the equation.
-1x + x + x2 = 100 + -1x + x

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

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

Solving
x2 = 100

Solving for variable 'x'.

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

Simplifying
x2 = 100

Take the square root of each side:
x = {-10, 10}