4A^2-2A-6=0

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

Simplifying
4A2 + -2A + -6 = 0

Reorder the terms:
-6 + -2A + 4A2 = 0

Solving
-6 + -2A + 4A2 = 0

Solving for variable 'A'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -1A + 2A2) = 0

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

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

Simplifying
-1 + -1A = 0

Solving
-1 + -1A = 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 + -1A = 0 + 1

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

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

Divide each side by '-1'.
A = -1

Simplifying
A = -1
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 = {-1, 1.5}