6a^2-14a=12

Solution for 6a^2-14a=12 equation:

Simplifying
6a2 + -14a = 12

Reorder the terms:
-14a + 6a2 = 12

Solving
-14a + 6a2 = 12

Solving for variable 'a'.

Reorder the terms:
-12 + -14a + 6a2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -14a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -7a + 3a2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -3a)' equal to zero and attempt to solve:

Simplifying
-2 + -3a = 0

Solving
-2 + -3a = 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 + -3a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3a = 0 + 2
-3a = 0 + 2

Combine like terms: 0 + 2 = 2
-3a = 2

Divide each side by '-3'.
a = -0.6666666667

Simplifying
a = -0.6666666667
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.6666666667, 3}