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

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

Simplifying
n(3 + n) = n(2) + 4n
(3 * n + n * n) = n(2) + 4n
(3n + n2) = n(2) + 4n

Reorder the terms for easier multiplication:
3n + n2 = 2n + 4n

Combine like terms: 2n + 4n = 6n
3n + n2 = 6n

Solving
3n + n2 = 6n

Solving for variable 'n'.

Reorder the terms:
3n + -6n + n2 = 6n + -6n

Combine like terms: 3n + -6n = -3n
-3n + n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
-3n + n2 = 0

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

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
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 = {0, 3}