2x^2-13x-189=0

Solution for 2x^2-13x-189=0 equation:

Simplifying
2x2 + -13x + -189 = 0

Reorder the terms:
-189 + -13x + 2x2 = 0

Solving
-189 + -13x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -1x)(27 + -2x) = 0

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(27 + -2x)' equal to zero and attempt to solve:

Simplifying
27 + -2x = 0

Solving
27 + -2x = 0

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

Add '-27' to each side of the equation.
27 + -27 + -2x = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -2x = 0 + -27
-2x = 0 + -27

Combine like terms: 0 + -27 = -27
-2x = -27

Divide each side by '-2'.
x = 13.5

Simplifying
x = 13.5
Solution
x = {-7, 13.5}