0=40000+300x-10x^2

Solution for 0=40000+300x-10x^2 equation:

Simplifying
0 = 40000 + 300x + -10x2

Solving
0 = 40000 + 300x + -10x2

Solving for variable 'x'.

Combine like terms: 0 + -40000 = -40000
-40000 + -300x + 10x2 = 40000 + 300x + -10x2 + -40000 + -300x + 10x2

Reorder the terms:
-40000 + -300x + 10x2 = 40000 + -40000 + 300x + -300x + -10x2 + 10x2

Combine like terms: 40000 + -40000 = 0
-40000 + -300x + 10x2 = 0 + 300x + -300x + -10x2 + 10x2
-40000 + -300x + 10x2 = 300x + -300x + -10x2 + 10x2

Combine like terms: 300x + -300x = 0
-40000 + -300x + 10x2 = 0 + -10x2 + 10x2
-40000 + -300x + 10x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
-40000 + -300x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-4000 + -30x + x2) = 0

Factor a trinomial.
10((-50 + -1x)(80 + -1x)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-50 + -1x)' equal to zero and attempt to solve:

Simplifying
-50 + -1x = 0

Solving
-50 + -1x = 0

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

Add '50' to each side of the equation.
-50 + 50 + -1x = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -1x = 0 + 50
-1x = 0 + 50

Combine like terms: 0 + 50 = 50
-1x = 50

Divide each side by '-1'.
x = -50

Simplifying
x = -50
Subproblem 2
Set the factor '(80 + -1x)' equal to zero and attempt to solve:

Simplifying
80 + -1x = 0

Solving
80 + -1x = 0

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

Add '-80' to each side of the equation.
80 + -80 + -1x = 0 + -80

Combine like terms: 80 + -80 = 0
0 + -1x = 0 + -80
-1x = 0 + -80

Combine like terms: 0 + -80 = -80
-1x = -80

Divide each side by '-1'.
x = 80

Simplifying
x = 80
Solution
x = {-50, 80}