(5+x)(4000-400x)-2(4000-400x)=0

Solution for (5+x)(4000-400x)-2(4000-400x)=0 equation:

Simplifying
(5 + x)(4000 + -400x) + -2(4000 + -400x) = 0

Multiply (5 + x) * (4000 + -400x)
(5(4000 + -400x) + x(4000 + -400x)) + -2(4000 + -400x) = 0
((4000 * 5 + -400x * 5) + x(4000 + -400x)) + -2(4000 + -400x) = 0
((20000 + -2000x) + x(4000 + -400x)) + -2(4000 + -400x) = 0
(20000 + -2000x + (4000 * x + -400x * x)) + -2(4000 + -400x) = 0
(20000 + -2000x + (4000x + -400x2)) + -2(4000 + -400x) = 0

Combine like terms: -2000x + 4000x = 2000x
(20000 + 2000x + -400x2) + -2(4000 + -400x) = 0
20000 + 2000x + -400x2 + (4000 * -2 + -400x * -2) = 0
20000 + 2000x + -400x2 + (-8000 + 800x) = 0

Reorder the terms:
20000 + -8000 + 2000x + 800x + -400x2 = 0

Combine like terms: 20000 + -8000 = 12000
12000 + 2000x + 800x + -400x2 = 0

Combine like terms: 2000x + 800x = 2800x
12000 + 2800x + -400x2 = 0

Solving
12000 + 2800x + -400x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '400'.
400(30 + 7x + -1x2) = 0

Factor a trinomial.
400((10 + -1x)(3 + x)) = 0

Ignore the factor 400.
Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {10, -3}