1200=90x-200-x^2

Solution for 1200=90x-200-x^2 equation:

Simplifying
1200 = 90x + -200 + -1x2

Reorder the terms:
1200 = -200 + 90x + -1x2

Solving
1200 = -200 + 90x + -1x2

Solving for variable 'x'.

Combine like terms: 1200 + 200 = 1400
1400 + -90x + x2 = -200 + 90x + -1x2 + 200 + -90x + x2

Reorder the terms:
1400 + -90x + x2 = -200 + 200 + 90x + -90x + -1x2 + x2

Combine like terms: -200 + 200 = 0
1400 + -90x + x2 = 0 + 90x + -90x + -1x2 + x2
1400 + -90x + x2 = 90x + -90x + -1x2 + x2

Combine like terms: 90x + -90x = 0
1400 + -90x + x2 = 0 + -1x2 + x2
1400 + -90x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
1400 + -90x + x2 = 0

Factor a trinomial.
(20 + -1x)(70 + -1x) = 0

Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
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 = {20, 70}