12a^2-14a-20=0

Solution for 12a^2-14a-20=0 equation:

Simplifying
12a2 + -14a + -20 = 0

Reorder the terms:
-20 + -14a + 12a2 = 0

Solving
-20 + -14a + 12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -7a + 6a2) = 0

Factor a trinomial.
2((-5 + -6a)(2 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -6a)' equal to zero and attempt to solve:

Simplifying
-5 + -6a = 0

Solving
-5 + -6a = 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 + -6a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6a = 0 + 5
-6a = 0 + 5

Combine like terms: 0 + 5 = 5
-6a = 5

Divide each side by '-6'.
a = -0.8333333333

Simplifying
a = -0.8333333333
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

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

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-0.8333333333, 2}