(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.
(-3 + -2n)(4 + -1n) = 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 + -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
Solution
n = {-1.5, 4}