[3n+8][2n-1]=

Solution for [3n+8][2n-1]= equation:

Simplifying
[3n + 8][2n + -1] = 0

Reorder the terms:
[8 + 3n][2n + -1] = 0

Reorder the terms:
[8 + 3n][-1 + 2n] = 0

Multiply [8 + 3n] * [-1 + 2n]
[8[-1 + 2n] + 3n * [-1 + 2n]] = 0
[[-1 * 8 + 2n * 8] + 3n * [-1 + 2n]] = 0
[[-8 + 16n] + 3n * [-1 + 2n]] = 0
[-8 + 16n + [-1 * 3n + 2n * 3n]] = 0
[-8 + 16n + [-3n + 6n2]] = 0

Combine like terms: 16n + -3n = 13n
[-8 + 13n + 6n2] = 0

Solving
-8 + 13n + 6n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-8 + -3n)(1 + -2n) = 0

Subproblem 1
Set the factor '(-8 + -3n)' equal to zero and attempt to solve:

Simplifying
-8 + -3n = 0

Solving
-8 + -3n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3n = 0 + 8
-3n = 0 + 8

Combine like terms: 0 + 8 = 8
-3n = 8

Divide each side by '-3'.
n = -2.666666667

Simplifying
n = -2.666666667
Subproblem 2
Set the factor '(1 + -2n)' equal to zero and attempt to solve:

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

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

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

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Solution
n = {-2.666666667, 0.5}