(4a+3)(3a+1)=0

Solution for (4a+3)(3a+1)=0 equation:

Simplifying
(4a + 3)(3a + 1) = 0

Reorder the terms:
(3 + 4a)(3a + 1) = 0

Reorder the terms:
(3 + 4a)(1 + 3a) = 0

Multiply (3 + 4a) * (1 + 3a)
(3(1 + 3a) + 4a * (1 + 3a)) = 0
((1 * 3 + 3a * 3) + 4a * (1 + 3a)) = 0
((3 + 9a) + 4a * (1 + 3a)) = 0
(3 + 9a + (1 * 4a + 3a * 4a)) = 0
(3 + 9a + (4a + 12a2)) = 0

Combine like terms: 9a + 4a = 13a
(3 + 13a + 12a2) = 0

Solving
3 + 13a + 12a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + 4a)(1 + 3a) = 0

Subproblem 1
Set the factor '(3 + 4a)' equal to zero and attempt to solve:

Simplifying
3 + 4a = 0

Solving
3 + 4a = 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 + 4a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4a = 0 + -3
4a = 0 + -3

Combine like terms: 0 + -3 = -3
4a = -3

Divide each side by '4'.
a = -0.75

Simplifying
a = -0.75
Subproblem 2
Set the factor '(1 + 3a)' equal to zero and attempt to solve:

Simplifying
1 + 3a = 0

Solving
1 + 3a = 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 + 3a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3a = 0 + -1
3a = 0 + -1

Combine like terms: 0 + -1 = -1
3a = -1

Divide each side by '3'.
a = -0.3333333333

Simplifying
a = -0.3333333333
Solution
a = {-0.75, -0.3333333333}