2(6+2a-3a^2)-12=

Solution for 2(6+2a-3a^2)-12= equation:

Simplifying
2(6 + 2a + -3a2) + -12 = 0
(6 * 2 + 2a * 2 + -3a2 * 2) + -12 = 0
(12 + 4a + -6a2) + -12 = 0

Reorder the terms:
12 + -12 + 4a + -6a2 = 0

Combine like terms: 12 + -12 = 0
0 + 4a + -6a2 = 0
4a + -6a2 = 0

Solving
4a + -6a2 = 0

Solving for variable 'a'.

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

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
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
Solution
a = {0, 0.6666666667}