(4a+3)(a+2)=0

Solution for (4a+3)(a+2)=0 equation:

Simplifying
(4a + 3)(a + 2) = 0

Reorder the terms:
(3 + 4a)(a + 2) = 0

Reorder the terms:
(3 + 4a)(2 + a) = 0

Multiply (3 + 4a) * (2 + a)
(3(2 + a) + 4a * (2 + a)) = 0
((2 * 3 + a * 3) + 4a * (2 + a)) = 0
((6 + 3a) + 4a * (2 + a)) = 0
(6 + 3a + (2 * 4a + a * 4a)) = 0
(6 + 3a + (8a + 4a2)) = 0

Combine like terms: 3a + 8a = 11a
(6 + 11a + 4a2) = 0

Solving
6 + 11a + 4a2 = 0

Solving for variable 'a'.

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

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

Simplifying
2 + a = 0

Solving
2 + a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

Simplifying
a = -2
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 = {-2, -0.75}