x^2-17x-138=0

Solution for x^2-17x-138=0 equation:

Simplifying
x2 + -17x + -138 = 0

Reorder the terms:
-138 + -17x + x2 = 0

Solving
-138 + -17x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(23 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(23 + -1x)' equal to zero and attempt to solve:

Simplifying
23 + -1x = 0

Solving
23 + -1x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -1x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -1x = 0 + -23
-1x = 0 + -23

Combine like terms: 0 + -23 = -23
-1x = -23

Divide each side by '-1'.
x = 23

Simplifying
x = 23
Solution
x = {-6, 23}