12x^2-10x-78=0

Solution for 12x^2-10x-78=0 equation:

Simplifying
12x2 + -10x + -78 = 0

Reorder the terms:
-78 + -10x + 12x2 = 0

Solving
-78 + -10x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-39 + -5x + 6x2) = 0

Factor a trinomial.
2((-13 + -6x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + -6x)' equal to zero and attempt to solve:

Simplifying
-13 + -6x = 0

Solving
-13 + -6x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -6x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -6x = 0 + 13
-6x = 0 + 13

Combine like terms: 0 + 13 = 13
-6x = 13

Divide each side by '-6'.
x = -2.166666667

Simplifying
x = -2.166666667
Subproblem 2
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
Solution
x = {-2.166666667, 3}