-x^2+690x-54000=0

Solution for -x^2+690x-54000=0 equation:

Simplifying
-1x2 + 690x + -54000 = 0

Reorder the terms:
-54000 + 690x + -1x2 = 0

Solving
-54000 + 690x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-600 + x)(90 + -1x) = 0

Subproblem 1
Set the factor '(-600 + x)' equal to zero and attempt to solve:

Simplifying
-600 + x = 0

Solving
-600 + x = 0

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

Add '600' to each side of the equation.
-600 + 600 + x = 0 + 600

Combine like terms: -600 + 600 = 0
0 + x = 0 + 600
x = 0 + 600

Combine like terms: 0 + 600 = 600
x = 600

Simplifying
x = 600
Subproblem 2
Set the factor '(90 + -1x)' equal to zero and attempt to solve:

Simplifying
90 + -1x = 0

Solving
90 + -1x = 0

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

Add '-90' to each side of the equation.
90 + -90 + -1x = 0 + -90

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

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

Divide each side by '-1'.
x = 90

Simplifying
x = 90
Solution
x = {600, 90}