-x^2+20x-19=0

Solution for -x^2+20x-19=0 equation:

Simplifying
-1x2 + 20x + -19 = 0

Reorder the terms:
-19 + 20x + -1x2 = 0

Solving
-19 + 20x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-19 + x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-19 + x)' equal to zero and attempt to solve:

Simplifying
-19 + x = 0

Solving
-19 + x = 0

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

Add '19' to each side of the equation.
-19 + 19 + x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + x = 0 + 19
x = 0 + 19

Combine like terms: 0 + 19 = 19
x = 19

Simplifying
x = 19
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {19, 1}