0=-4a^2-2a+12

Solution for 0=-4a^2-2a+12 equation:

Simplifying
0 = -4a2 + -2a + 12

Reorder the terms:
0 = 12 + -2a + -4a2

Solving
0 = 12 + -2a + -4a2

Solving for variable 'a'.

Combine like terms: 0 + -12 = -12
-12 + 2a + 4a2 = 12 + -2a + -4a2 + -12 + 2a + 4a2

Reorder the terms:
-12 + 2a + 4a2 = 12 + -12 + -2a + 2a + -4a2 + 4a2

Combine like terms: 12 + -12 = 0
-12 + 2a + 4a2 = 0 + -2a + 2a + -4a2 + 4a2
-12 + 2a + 4a2 = -2a + 2a + -4a2 + 4a2

Combine like terms: -2a + 2a = 0
-12 + 2a + 4a2 = 0 + -4a2 + 4a2
-12 + 2a + 4a2 = -4a2 + 4a2

Combine like terms: -4a2 + 4a2 = 0
-12 + 2a + 4a2 = 0

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

Factor a trinomial.
2((-2 + -1a)(3 + -2a)) = 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 '(3 + -2a)' equal to zero and attempt to solve:

Simplifying
3 + -2a = 0

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

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

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

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Solution
a = {-2, 1.5}