(3n+1)(2n+5)=

Solution for (3n+1)(2n+5)= equation:

Simplifying
(3n + 1)(2n + 5) = 0

Reorder the terms:
(1 + 3n)(2n + 5) = 0

Reorder the terms:
(1 + 3n)(5 + 2n) = 0

Multiply (1 + 3n) * (5 + 2n)
(1(5 + 2n) + 3n * (5 + 2n)) = 0
((5 * 1 + 2n * 1) + 3n * (5 + 2n)) = 0
((5 + 2n) + 3n * (5 + 2n)) = 0
(5 + 2n + (5 * 3n + 2n * 3n)) = 0
(5 + 2n + (15n + 6n2)) = 0

Combine like terms: 2n + 15n = 17n
(5 + 17n + 6n2) = 0

Solving
5 + 17n + 6n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(5 + 2n)(1 + 3n) = 0

Subproblem 1
Set the factor '(5 + 2n)' equal to zero and attempt to solve:

Simplifying
5 + 2n = 0

Solving
5 + 2n = 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 + 2n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2n = 0 + -5
2n = 0 + -5

Combine like terms: 0 + -5 = -5
2n = -5

Divide each side by '2'.
n = -2.5

Simplifying
n = -2.5
Subproblem 2
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
Solution
n = {-2.5, -0.3333333333}