0=550(x)-(10000+30x+x^2)

Solution for 0=550(x)-(10000+30x+x^2) equation:

Simplifying
0 = 550(x) + -1(10000 + 30x + x2)
0 = 550x + (10000 * -1 + 30x * -1 + x2 * -1)
0 = 550x + (-10000 + -30x + -1x2)

Reorder the terms:
0 = -10000 + 550x + -30x + -1x2

Combine like terms: 550x + -30x = 520x
0 = -10000 + 520x + -1x2

Solving
0 = -10000 + 520x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 10000 = 10000
10000 + -520x + x2 = -10000 + 520x + -1x2 + 10000 + -520x + x2

Reorder the terms:
10000 + -520x + x2 = -10000 + 10000 + 520x + -520x + -1x2 + x2

Combine like terms: -10000 + 10000 = 0
10000 + -520x + x2 = 0 + 520x + -520x + -1x2 + x2
10000 + -520x + x2 = 520x + -520x + -1x2 + x2

Combine like terms: 520x + -520x = 0
10000 + -520x + x2 = 0 + -1x2 + x2
10000 + -520x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
10000 + -520x + x2 = 0

Factor a trinomial.
(20 + -1x)(500 + -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 '(500 + -1x)' equal to zero and attempt to solve:

Simplifying
500 + -1x = 0

Solving
500 + -1x = 0

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

Add '-500' to each side of the equation.
500 + -500 + -1x = 0 + -500

Combine like terms: 500 + -500 = 0
0 + -1x = 0 + -500
-1x = 0 + -500

Combine like terms: 0 + -500 = -500
-1x = -500

Divide each side by '-1'.
x = 500

Simplifying
x = 500
Solution
x = {20, 500}