0=-x^2+80x+900

Solution for 0=-x^2+80x+900 equation:

Simplifying
0 = -1x2 + 80x + 900

Reorder the terms:
0 = 900 + 80x + -1x2

Solving
0 = 900 + 80x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -900 = -900
-900 + -80x + x2 = 900 + 80x + -1x2 + -900 + -80x + x2

Reorder the terms:
-900 + -80x + x2 = 900 + -900 + 80x + -80x + -1x2 + x2

Combine like terms: 900 + -900 = 0
-900 + -80x + x2 = 0 + 80x + -80x + -1x2 + x2
-900 + -80x + x2 = 80x + -80x + -1x2 + x2

Combine like terms: 80x + -80x = 0
-900 + -80x + x2 = 0 + -1x2 + x2
-900 + -80x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-900 + -80x + x2 = 0

Factor a trinomial.
(-10 + -1x)(90 + -1x) = 0

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 '(90 + -1x)' equal to zero and attempt to solve:

Simplifying
90 + -1x = 0

Solving
90 + -1x = 0

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

Add '-90' to each side of the equation.
90 + -90 + -1x = 0 + -90

Combine like terms: 90 + -90 = 0
0 + -1x = 0 + -90
-1x = 0 + -90

Combine like terms: 0 + -90 = -90
-1x = -90

Divide each side by '-1'.
x = 90

Simplifying
x = 90
Solution
x = {-10, 90}