2(5n+3)(n+7)=0

Solution for 2(5n+3)(n+7)=0 equation:

Simplifying
2(5n + 3)(n + 7) = 0

Reorder the terms:
2(3 + 5n)(n + 7) = 0

Reorder the terms:
2(3 + 5n)(7 + n) = 0

Multiply (3 + 5n) * (7 + n)
2(3(7 + n) + 5n * (7 + n)) = 0
2((7 * 3 + n * 3) + 5n * (7 + n)) = 0
2((21 + 3n) + 5n * (7 + n)) = 0
2(21 + 3n + (7 * 5n + n * 5n)) = 0
2(21 + 3n + (35n + 5n2)) = 0

Combine like terms: 3n + 35n = 38n
2(21 + 38n + 5n2) = 0
(21 * 2 + 38n * 2 + 5n2 * 2) = 0
(42 + 76n + 10n2) = 0

Solving
42 + 76n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 38n + 5n2) = 0

Factor a trinomial.
2((7 + n)(3 + 5n)) = 0

Ignore the factor 2.
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 '(3 + 5n)' equal to zero and attempt to solve:

Simplifying
3 + 5n = 0

Solving
3 + 5n = 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 + 5n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5n = 0 + -3
5n = 0 + -3

Combine like terms: 0 + -3 = -3
5n = -3

Divide each side by '5'.
n = -0.6

Simplifying
n = -0.6
Solution
n = {-7, -0.6}