0=x^2-8x-209

Solution for 0=x^2-8x-209 equation:

Simplifying
0 = x2 + -8x + -209

Reorder the terms:
0 = -209 + -8x + x2

Solving
0 = -209 + -8x + x2

Solving for variable 'x'.

Combine like terms: 0 + 209 = 209
209 + 8x + -1x2 = -209 + -8x + x2 + 209 + 8x + -1x2

Reorder the terms:
209 + 8x + -1x2 = -209 + 209 + -8x + 8x + x2 + -1x2

Combine like terms: -209 + 209 = 0
209 + 8x + -1x2 = 0 + -8x + 8x + x2 + -1x2
209 + 8x + -1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
209 + 8x + -1x2 = 0 + x2 + -1x2
209 + 8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
209 + 8x + -1x2 = 0

Factor a trinomial.
(19 + -1x)(11 + x) = 0

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

Simplifying
19 + -1x = 0

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

Combine like terms: 19 + -19 = 0
0 + -1x = 0 + -19
-1x = 0 + -19

Combine like terms: 0 + -19 = -19
-1x = -19

Divide each side by '-1'.
x = 19

Simplifying
x = 19
Subproblem 2
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11
Solution
x = {19, -11}