2400=(1000-100x)x

Solution for 2400=(1000-100x)x equation:

Simplifying
2400 = (1000 + -100x) * x

Reorder the terms for easier multiplication:
2400 = x(1000 + -100x)
2400 = (1000 * x + -100x * x)
2400 = (1000x + -100x2)

Solving
2400 = 1000x + -100x2

Solving for variable 'x'.

Reorder the terms:
2400 + -1000x + 100x2 = 1000x + -1000x + -100x2 + 100x2

Combine like terms: 1000x + -1000x = 0
2400 + -1000x + 100x2 = 0 + -100x2 + 100x2
2400 + -1000x + 100x2 = -100x2 + 100x2

Combine like terms: -100x2 + 100x2 = 0
2400 + -1000x + 100x2 = 0

Factor out the Greatest Common Factor (GCF), '100'.
100(24 + -10x + x2) = 0

Factor a trinomial.
100((4 + -1x)(6 + -1x)) = 0

Ignore the factor 100.
Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {4, 6}