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

Solution for 0=(n+3)(2n+1) equation:

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

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

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

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

Combine like terms: 6n + 1n = 7n
0 = (3 + 7n + 2n2)

Solving
0 = 3 + 7n + 2n2

Solving for variable 'n'.

Combine like terms: 0 + -3 = -3
-3 + -7n + -2n2 = 3 + 7n + 2n2 + -3 + -7n + -2n2

Reorder the terms:
-3 + -7n + -2n2 = 3 + -3 + 7n + -7n + 2n2 + -2n2

Combine like terms: 3 + -3 = 0
-3 + -7n + -2n2 = 0 + 7n + -7n + 2n2 + -2n2
-3 + -7n + -2n2 = 7n + -7n + 2n2 + -2n2

Combine like terms: 7n + -7n = 0
-3 + -7n + -2n2 = 0 + 2n2 + -2n2
-3 + -7n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-3 + -7n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 7n + 2n2) = 0

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

Ignore the factor -1.
Subproblem 1
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
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 = {-3, -0.5}