5(2+n)-3n(2+n)=

Solution for 5(2+n)-3n(2+n)= equation:

Simplifying
5(2 + n) + -3n(2 + n) = 0
(2 * 5 + n * 5) + -3n(2 + n) = 0
(10 + 5n) + -3n(2 + n) = 0
10 + 5n + (2 * -3n + n * -3n) = 0
10 + 5n + (-6n + -3n2) = 0

Combine like terms: 5n + -6n = -1n
10 + -1n + -3n2 = 0

Solving
10 + -1n + -3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(5 + -3n)(2 + n) = 0

Subproblem 1
Set the factor '(5 + -3n)' equal to zero and attempt to solve:

Simplifying
5 + -3n = 0

Solving
5 + -3n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3n = 0 + -5
-3n = 0 + -5

Combine like terms: 0 + -5 = -5
-3n = -5

Divide each side by '-3'.
n = 1.666666667

Simplifying
n = 1.666666667
Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 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 + n = 0 + -2

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

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

Simplifying
n = -2
Solution
n = {1.666666667, -2}