800=-x^2+72x+80

Solution for 800=-x^2+72x+80 equation:

Simplifying
800 = -1x2 + 72x + 80

Reorder the terms:
800 = 80 + 72x + -1x2

Solving
800 = 80 + 72x + -1x2

Solving for variable 'x'.

Combine like terms: 800 + -80 = 720
720 + -72x + x2 = 80 + 72x + -1x2 + -80 + -72x + x2

Reorder the terms:
720 + -72x + x2 = 80 + -80 + 72x + -72x + -1x2 + x2

Combine like terms: 80 + -80 = 0
720 + -72x + x2 = 0 + 72x + -72x + -1x2 + x2
720 + -72x + x2 = 72x + -72x + -1x2 + x2

Combine like terms: 72x + -72x = 0
720 + -72x + x2 = 0 + -1x2 + x2
720 + -72x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
720 + -72x + x2 = 0

Factor a trinomial.
(12 + -1x)(60 + -1x) = 0

Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Subproblem 2
Set the factor '(60 + -1x)' equal to zero and attempt to solve:

Simplifying
60 + -1x = 0

Solving
60 + -1x = 0

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

Add '-60' to each side of the equation.
60 + -60 + -1x = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -1x = 0 + -60
-1x = 0 + -60

Combine like terms: 0 + -60 = -60
-1x = -60

Divide each side by '-1'.
x = 60

Simplifying
x = 60
Solution
x = {12, 60}