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

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

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

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

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

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

Combine like terms: 4n + -3n = 1n
4(-12 + 1n + n2) = 0
(-12 * 4 + 1n * 4 + n2 * 4) = 0
(-48 + 4n + 4n2) = 0

Solving
-48 + 4n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + n + n2) = 0

Factor a trinomial.
4((-4 + -1n)(3 + -1n)) = 0

Ignore the factor 4.
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 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-4, 3}