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

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

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

Reorder the terms:
(-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.
(-4 + -1n)(3 + -2n) = 0

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

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 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 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
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
Solution
n = {-4, 1.5}