80=24x-x^2

Solution for 80=24x-x^2 equation:

Simplifying
80 = 24x + -1x2

Solving
80 = 24x + -1x2

Solving for variable 'x'.

Reorder the terms:
80 + -24x + x2 = 24x + -24x + -1x2 + x2

Combine like terms: 24x + -24x = 0
80 + -24x + x2 = 0 + -1x2 + x2
80 + -24x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
80 + -24x + x2 = 0

Factor a trinomial.
(4 + -1x)(20 + -1x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
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
Solution
x = {4, 20}