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

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

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

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

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

Combine like terms: 3n + -8n = -5n
(12 + -5n + -2n2) = 0

Solving
12 + -5n + -2n2 = 0

Solving for variable 'n'.

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

Subproblem 1
Set the factor '(3 + -2n)' equal to zero and attempt to solve:

Simplifying
3 + -2n = 0

Solving
3 + -2n = 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 + -2n = 0 + -3

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

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

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
Subproblem 2
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

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

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

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

Simplifying
n = -4
Solution
n = {1.5, -4}