4200=(1300-100x)x

Solution for 4200=(1300-100x)x equation:

Simplifying
4200 = (1300 + -100x) * x

Reorder the terms for easier multiplication:
4200 = x(1300 + -100x)
4200 = (1300 * x + -100x * x)
4200 = (1300x + -100x2)

Solving
4200 = 1300x + -100x2

Solving for variable 'x'.

Reorder the terms:
4200 + -1300x + 100x2 = 1300x + -1300x + -100x2 + 100x2

Combine like terms: 1300x + -1300x = 0
4200 + -1300x + 100x2 = 0 + -100x2 + 100x2
4200 + -1300x + 100x2 = -100x2 + 100x2

Combine like terms: -100x2 + 100x2 = 0
4200 + -1300x + 100x2 = 0

Factor out the Greatest Common Factor (GCF), '100'.
100(42 + -13x + x2) = 0

Factor a trinomial.
100((6 + -1x)(7 + -1x)) = 0

Ignore the factor 100.
Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {6, 7}