x(90-x)=1800

Solution for x(90-x)=1800 equation:

Simplifying
x(90 + -1x) = 1800
(90 * x + -1x * x) = 1800
(90x + -1x2) = 1800

Solving
90x + -1x2 = 1800

Solving for variable 'x'.

Reorder the terms:
-1800 + 90x + -1x2 = 1800 + -1800

Combine like terms: 1800 + -1800 = 0
-1800 + 90x + -1x2 = 0

Factor a trinomial.
(-60 + x)(30 + -1x) = 0

Subproblem 1
Set the factor '(-60 + x)' equal to zero and attempt to solve:

Simplifying
-60 + x = 0

Solving
-60 + x = 0

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

Add '60' to each side of the equation.
-60 + 60 + x = 0 + 60

Combine like terms: -60 + 60 = 0
0 + x = 0 + 60
x = 0 + 60

Combine like terms: 0 + 60 = 60
x = 60

Simplifying
x = 60
Subproblem 2
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
Solution
x = {60, 30}