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

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

Simplifying
5n + 3 = 2(n + 2) * 3n

Reorder the terms:
3 + 5n = 2(n + 2) * 3n

Reorder the terms:
3 + 5n = 2(2 + n) * 3n

Reorder the terms for easier multiplication:
3 + 5n = 2 * 3n(2 + n)

Multiply 2 * 3
3 + 5n = 6n(2 + n)
3 + 5n = (2 * 6n + n * 6n)
3 + 5n = (12n + 6n2)

Solving
3 + 5n = 12n + 6n2

Solving for variable 'n'.

Combine like terms: 5n + -12n = -7n
3 + -7n + -6n2 = 12n + 6n2 + -12n + -6n2

Reorder the terms:
3 + -7n + -6n2 = 12n + -12n + 6n2 + -6n2

Combine like terms: 12n + -12n = 0
3 + -7n + -6n2 = 0 + 6n2 + -6n2
3 + -7n + -6n2 = 6n2 + -6n2

Combine like terms: 6n2 + -6n2 = 0
3 + -7n + -6n2 = 0

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

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

Simplifying
1 + -3n = 0

Solving
1 + -3n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3n = 0 + -1

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

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

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Subproblem 2
Set the factor '(3 + 2n)' equal to zero and attempt to solve:

Simplifying
3 + 2n = 0

Solving
3 + 2n = 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 + 2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2n = 0 + -3
2n = 0 + -3

Combine like terms: 0 + -3 = -3
2n = -3

Divide each side by '2'.
n = -1.5

Simplifying
n = -1.5
Solution
n = {0.3333333333, -1.5}