0=-x^2+16x-39

Solution for 0=-x^2+16x-39 equation:

Simplifying
0 = -1x2 + 16x + -39

Reorder the terms:
0 = -39 + 16x + -1x2

Solving
0 = -39 + 16x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 39 = 39
39 + -16x + x2 = -39 + 16x + -1x2 + 39 + -16x + x2

Reorder the terms:
39 + -16x + x2 = -39 + 39 + 16x + -16x + -1x2 + x2

Combine like terms: -39 + 39 = 0
39 + -16x + x2 = 0 + 16x + -16x + -1x2 + x2
39 + -16x + x2 = 16x + -16x + -1x2 + x2

Combine like terms: 16x + -16x = 0
39 + -16x + x2 = 0 + -1x2 + x2
39 + -16x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
39 + -16x + x2 = 0

Factor a trinomial.
(3 + -1x)(13 + -1x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {3, 13}