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

Solution for 6(n-3)3(n+4)= equation:

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

Reorder the terms:
6(-3 + n) * 3(n + 4) = 0

Reorder the terms:
6(-3 + n) * 3(4 + n) = 0

Reorder the terms for easier multiplication:
6 * 3(-3 + n)(4 + n) = 0

Multiply 6 * 3
18(-3 + n)(4 + n) = 0

Multiply (-3 + n) * (4 + n)
18(-3(4 + n) + n(4 + n)) = 0
18((4 * -3 + n * -3) + n(4 + n)) = 0
18((-12 + -3n) + n(4 + n)) = 0
18(-12 + -3n + (4 * n + n * n)) = 0
18(-12 + -3n + (4n + n2)) = 0

Combine like terms: -3n + 4n = 1n
18(-12 + 1n + n2) = 0
(-12 * 18 + 1n * 18 + n2 * 18) = 0
(-216 + 18n + 18n2) = 0

Solving
-216 + 18n + 18n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '18'.
18(-12 + n + n2) = 0

Factor a trinomial.
18((-4 + -1n)(3 + -1n)) = 0

Ignore the factor 18.
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}