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

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

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

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

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

Multiply (2 + 3n) * (3 + 4n)
(2(3 + 4n) + 3n * (3 + 4n)) = 0
((3 * 2 + 4n * 2) + 3n * (3 + 4n)) = 0
((6 + 8n) + 3n * (3 + 4n)) = 0
(6 + 8n + (3 * 3n + 4n * 3n)) = 0
(6 + 8n + (9n + 12n2)) = 0

Combine like terms: 8n + 9n = 17n
(6 + 17n + 12n2) = 0

Solving
6 + 17n + 12n2 = 0

Solving for variable 'n'.

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

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

Simplifying
3 + 4n = 0

Solving
3 + 4n = 0

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

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

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

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

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

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

Simplifying
2 + 3n = 0

Solving
2 + 3n = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3n = 0 + -2
3n = 0 + -2

Combine like terms: 0 + -2 = -2
3n = -2

Divide each side by '3'.
n = -0.6666666667

Simplifying
n = -0.6666666667
Solution
n = {-0.75, -0.6666666667}