0=4a^2-2a-6

Solution for 0=4a^2-2a-6 equation:

Simplifying
0 = 4a2 + -2a + -6

Reorder the terms:
0 = -6 + -2a + 4a2

Solving
0 = -6 + -2a + 4a2

Solving for variable 'a'.

Combine like terms: 0 + 6 = 6
6 + 2a + -4a2 = -6 + -2a + 4a2 + 6 + 2a + -4a2

Reorder the terms:
6 + 2a + -4a2 = -6 + 6 + -2a + 2a + 4a2 + -4a2

Combine like terms: -6 + 6 = 0
6 + 2a + -4a2 = 0 + -2a + 2a + 4a2 + -4a2
6 + 2a + -4a2 = -2a + 2a + 4a2 + -4a2

Combine like terms: -2a + 2a = 0
6 + 2a + -4a2 = 0 + 4a2 + -4a2
6 + 2a + -4a2 = 4a2 + -4a2

Combine like terms: 4a2 + -4a2 = 0
6 + 2a + -4a2 = 0

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

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

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

Simplifying
1 + a = 0

Solving
1 + a = 0

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

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

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

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

Simplifying
a = -1
Solution
a = {1.5, -1}