410x-4000-x^2=0

Solution for 410x-4000-x^2=0 equation:

Simplifying
410x + -4000 + -1x2 = 0

Reorder the terms:
-4000 + 410x + -1x2 = 0

Solving
-4000 + 410x + -1x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-400 + x = 0

Solving
-400 + x = 0

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

Add '400' to each side of the equation.
-400 + 400 + x = 0 + 400

Combine like terms: -400 + 400 = 0
0 + x = 0 + 400
x = 0 + 400

Combine like terms: 0 + 400 = 400
x = 400

Simplifying
x = 400
Subproblem 2
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
Solution
x = {400, 10}