4n+11n=n*(n+n)

Solution for 4n+11n=n*(n+n) equation:

Simplifying
4n + 11n = n(n + n)

Combine like terms: 4n + 11n = 15n
15n = n(n + n)

Combine like terms: n + n = 2n
15n = n(2n)

Remove parenthesis around (2n)
15n = n * 2n

Reorder the terms for easier multiplication:
15n = 2n * n

Multiply n * n
15n = 2n2

Solving
15n = 2n2

Solving for variable 'n'.

Combine like terms: 2n2 + -2n2 = 0
15n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(15 + -2n) = 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 '(15 + -2n)' equal to zero and attempt to solve:

Simplifying
15 + -2n = 0

Solving
15 + -2n = 0

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

Add '-15' to each side of the equation.
15 + -15 + -2n = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2n = 0 + -15
-2n = 0 + -15

Combine like terms: 0 + -15 = -15
-2n = -15

Divide each side by '-2'.
n = 7.5

Simplifying
n = 7.5
Solution
n = {0, 7.5}