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

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

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

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

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

Multiply (3 + 4x) * (2 + x)
(3(2 + x) + 4x * (2 + x)) = 0
((2 * 3 + x * 3) + 4x * (2 + x)) = 0
((6 + 3x) + 4x * (2 + x)) = 0
(6 + 3x + (2 * 4x + x * 4x)) = 0
(6 + 3x + (8x + 4x2)) = 0

Combine like terms: 3x + 8x = 11x
(6 + 11x + 4x2) = 0

Solving
6 + 11x + 4x2 = 0

Solving for variable 'x'.

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

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Subproblem 2
Set the factor '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4x = 0 + -3

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

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

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

Simplifying
x = -0.75
Solution
x = {-2, -0.75}