(n+7)(2n+1)=0

Solution for (n+7)(2n+1)=0 equation:

Simplifying
(n + 7)(2n + 1) = 0

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

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

Multiply (7 + n) * (1 + 2n)
(7(1 + 2n) + n(1 + 2n)) = 0
((1 * 7 + 2n * 7) + n(1 + 2n)) = 0
((7 + 14n) + n(1 + 2n)) = 0
(7 + 14n + (1 * n + 2n * n)) = 0
(7 + 14n + (1n + 2n2)) = 0

Combine like terms: 14n + 1n = 15n
(7 + 15n + 2n2) = 0

Solving
7 + 15n + 2n2 = 0

Solving for variable 'n'.

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

Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve:

Simplifying
7 + n = 0

Solving
7 + n = 0

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

Add '-7' to each side of the equation.
7 + -7 + n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + n = 0 + -7
n = 0 + -7

Combine like terms: 0 + -7 = -7
n = -7

Simplifying
n = -7
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 = {-7, -0.5}