4n+6-2n=n(n+3)

Solution for 4n+6-2n=n(n+3) equation:

Simplifying
4n + 6 + -2n = n(n + 3)

Reorder the terms:
6 + 4n + -2n = n(n + 3)

Combine like terms: 4n + -2n = 2n
6 + 2n = n(n + 3)

Reorder the terms:
6 + 2n = n(3 + n)
6 + 2n = (3 * n + n * n)
6 + 2n = (3n + n2)

Solving
6 + 2n = 3n + n2

Solving for variable 'n'.

Combine like terms: 2n + -3n = -1n
6 + -1n + -1n2 = 3n + n2 + -3n + -1n2

Reorder the terms:
6 + -1n + -1n2 = 3n + -3n + n2 + -1n2

Combine like terms: 3n + -3n = 0
6 + -1n + -1n2 = 0 + n2 + -1n2
6 + -1n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
6 + -1n + -1n2 = 0

Factor a trinomial.
(2 + -1n)(3 + n) = 0

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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
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 = {2, -3}