4a^2x^2+8ax+3=0

Solution for 4a^2x^2+8ax+3=0 equation:

Simplifying
4a2x2 + 8ax + 3 = 0

Reorder the terms:
3 + 8ax + 4a2x2 = 0

Solving
3 + 8ax + 4a2x2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(3 + 2ax)' equal to zero and attempt to solve:

Simplifying
3 + 2ax = 0

Solving
3 + 2ax = 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 + 2ax = 0 + -3

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

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

Divide each side by '2x'.
a = -1.5x-1

Simplifying
a = -1.5x-1
Subproblem 2
Set the factor '(1 + 2ax)' equal to zero and attempt to solve:

Simplifying
1 + 2ax = 0

Solving
1 + 2ax = 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 + 2ax = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2ax = 0 + -1
2ax = 0 + -1

Combine like terms: 0 + -1 = -1
2ax = -1

Divide each side by '2x'.
a = -0.5x-1

Simplifying
a = -0.5x-1
Solution
a = {-1.5x-1, -0.5x-1}