-52+12a^2-2a=0

Solution for -52+12a^2-2a=0 equation:

Simplifying
-52 + 12a2 + -2a = 0

Reorder the terms:
-52 + -2a + 12a2 = 0

Solving
-52 + -2a + 12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-26 + -1a + 6a2) = 0

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

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

Simplifying
13 + -6a = 0

Solving
13 + -6a = 0

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

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

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

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

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

Simplifying
a = 2.166666667
Solution
a = {-2, 2.166666667}