2n+3n+4n=n*n

Solution for 2n+3n+4n=n*n equation:

Simplifying
2n + 3n + 4n = n * n

Combine like terms: 2n + 3n = 5n
5n + 4n = n * n

Combine like terms: 5n + 4n = 9n
9n = n * n

Multiply n * n
9n = n2

Solving
9n = n2

Solving for variable 'n'.

Combine like terms: n2 + -1n2 = 0
9n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(9 + -1n) = 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 '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {0, 9}