4200=200x-2x^2

Solution for 4200=200x-2x^2 equation:

Simplifying
4200 = 200x + -2x2

Solving
4200 = 200x + -2x2

Solving for variable 'x'.

Reorder the terms:
4200 + -200x + 2x2 = 200x + -200x + -2x2 + 2x2

Combine like terms: 200x + -200x = 0
4200 + -200x + 2x2 = 0 + -2x2 + 2x2
4200 + -200x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
4200 + -200x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2100 + -100x + x2) = 0

Factor a trinomial.
2((30 + -1x)(70 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Subproblem 2
Set the factor '(70 + -1x)' equal to zero and attempt to solve:

Simplifying
70 + -1x = 0

Solving
70 + -1x = 0

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

Add '-70' to each side of the equation.
70 + -70 + -1x = 0 + -70

Combine like terms: 70 + -70 = 0
0 + -1x = 0 + -70
-1x = 0 + -70

Combine like terms: 0 + -70 = -70
-1x = -70

Divide each side by '-1'.
x = 70

Simplifying
x = 70
Solution
x = {30, 70}