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

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

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

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

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

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

Combine like terms: 3a + 4a = 7a
(3 + 7a + 4a2) = 0

Solving
3 + 7a + 4a2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
Subproblem 2
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
Solution
a = {-1, -0.75}