40x-x^2=384

Solution for 40x-x^2=384 equation:

Simplifying
40x + -1x2 = 384

Solving
40x + -1x2 = 384

Solving for variable 'x'.

Reorder the terms:
-384 + 40x + -1x2 = 384 + -384

Combine like terms: 384 + -384 = 0
-384 + 40x + -1x2 = 0

Factor a trinomial.
(-24 + x)(16 + -1x) = 0

Subproblem 1
Set the factor '(-24 + x)' equal to zero and attempt to solve:

Simplifying
-24 + x = 0

Solving
-24 + x = 0

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

Add '24' to each side of the equation.
-24 + 24 + x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + x = 0 + 24
x = 0 + 24

Combine like terms: 0 + 24 = 24
x = 24

Simplifying
x = 24
Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {24, 16}