16(n+3)=4(12+4n)n

Solution for 16(n+3)=4(12+4n)n equation:

Simplifying
16(n + 3) = 4(12 + 4n) * n

Reorder the terms:
16(3 + n) = 4(12 + 4n) * n
(3 * 16 + n * 16) = 4(12 + 4n) * n
(48 + 16n) = 4(12 + 4n) * n

Reorder the terms for easier multiplication:
48 + 16n = 4n(12 + 4n)
48 + 16n = (12 * 4n + 4n * 4n)
48 + 16n = (48n + 16n2)

Solving
48 + 16n = 48n + 16n2

Solving for variable 'n'.

Combine like terms: 16n + -48n = -32n
48 + -32n + -16n2 = 48n + 16n2 + -48n + -16n2

Reorder the terms:
48 + -32n + -16n2 = 48n + -48n + 16n2 + -16n2

Combine like terms: 48n + -48n = 0
48 + -32n + -16n2 = 0 + 16n2 + -16n2
48 + -32n + -16n2 = 16n2 + -16n2

Combine like terms: 16n2 + -16n2 = 0
48 + -32n + -16n2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(3 + -2n + -1n2) = 0

Factor a trinomial.
16((1 + -1n)(3 + n)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

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

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

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

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

Simplifying
3 + n = 0

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

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

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

Simplifying
n = -3
Solution
n = {1, -3}