(100-2x)x=800

Solution for (100-2x)x=800 equation:

Simplifying
(100 + -2x) * x = 800

Reorder the terms for easier multiplication:
x(100 + -2x) = 800
(100 * x + -2x * x) = 800
(100x + -2x2) = 800

Solving
100x + -2x2 = 800

Solving for variable 'x'.

Reorder the terms:
-800 + 100x + -2x2 = 800 + -800

Combine like terms: 800 + -800 = 0
-800 + 100x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-400 + 50x + -1x2) = 0

Factor a trinomial.
2((-40 + x)(10 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-40 + x)' equal to zero and attempt to solve:

Simplifying
-40 + x = 0

Solving
-40 + x = 0

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

Add '40' to each side of the equation.
-40 + 40 + x = 0 + 40

Combine like terms: -40 + 40 = 0
0 + x = 0 + 40
x = 0 + 40

Combine like terms: 0 + 40 = 40
x = 40

Simplifying
x = 40
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 = {40, 10}