(8a+3)(6a+1)=0

Solution for (8a+3)(6a+1)=0 equation:

Simplifying
(8a + 3)(6a + 1) = 0

Reorder the terms:
(3 + 8a)(6a + 1) = 0

Reorder the terms:
(3 + 8a)(1 + 6a) = 0

Multiply (3 + 8a) * (1 + 6a)
(3(1 + 6a) + 8a * (1 + 6a)) = 0
((1 * 3 + 6a * 3) + 8a * (1 + 6a)) = 0
((3 + 18a) + 8a * (1 + 6a)) = 0
(3 + 18a + (1 * 8a + 6a * 8a)) = 0
(3 + 18a + (8a + 48a2)) = 0

Combine like terms: 18a + 8a = 26a
(3 + 26a + 48a2) = 0

Solving
3 + 26a + 48a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + 8a)(1 + 6a) = 0

Subproblem 1
Set the factor '(3 + 8a)' equal to zero and attempt to solve:

Simplifying
3 + 8a = 0

Solving
3 + 8a = 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 + 8a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8a = 0 + -3
8a = 0 + -3

Combine like terms: 0 + -3 = -3
8a = -3

Divide each side by '8'.
a = -0.375

Simplifying
a = -0.375
Subproblem 2
Set the factor '(1 + 6a)' equal to zero and attempt to solve:

Simplifying
1 + 6a = 0

Solving
1 + 6a = 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 + 6a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6a = 0 + -1
6a = 0 + -1

Combine like terms: 0 + -1 = -1
6a = -1

Divide each side by '6'.
a = -0.1666666667

Simplifying
a = -0.1666666667
Solution
a = {-0.375, -0.1666666667}