6x^2-5x-69=0

Solution for 6x^2-5x-69=0 equation:

Simplifying
6x2 + -5x + -69 = 0

Reorder the terms:
-69 + -5x + 6x2 = 0

Solving
-69 + -5x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x)(23 + -6x) = 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 '(23 + -6x)' equal to zero and attempt to solve:

Simplifying
23 + -6x = 0

Solving
23 + -6x = 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 + -6x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -6x = 0 + -23
-6x = 0 + -23

Combine like terms: 0 + -23 = -23
-6x = -23

Divide each side by '-6'.
x = 3.833333333

Simplifying
x = 3.833333333
Solution
x = {-3, 3.833333333}