12a^2-14a-10=0

Solution for 12a^2-14a-10=0 equation:

Simplifying
12a2 + -14a + -10 = 0

Reorder the terms:
-10 + -14a + 12a2 = 0

Solving
-10 + -14a + 12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -7a + 6a2) = 0

Factor a trinomial.
2((-1 + -2a)(5 + -3a)) = 0

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

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2a = 0 + 1
-2a = 0 + 1

Combine like terms: 0 + 1 = 1
-2a = 1

Divide each side by '-2'.
a = -0.5

Simplifying
a = -0.5
Subproblem 2
Set the factor '(5 + -3a)' equal to zero and attempt to solve:

Simplifying
5 + -3a = 0

Solving
5 + -3a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3a = 0 + -5
-3a = 0 + -5

Combine like terms: 0 + -5 = -5
-3a = -5

Divide each side by '-3'.
a = 1.666666667

Simplifying
a = 1.666666667
Solution
a = {-0.5, 1.666666667}