(3n+4)(n+8)=0

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Solution for (3n+4)(n+8)=0 equation: 


Simplifying
(3n + 4)(n + 8) = 0

Reorder the terms:
(4 + 3n)(n + 8) = 0

Reorder the terms:
(4 + 3n)(8 + n) = 0

Multiply (4 + 3n) * (8 + n)
(4(8 + n) + 3n * (8 + n)) = 0
((8 * 4 + n * 4) + 3n * (8 + n)) = 0
((32 + 4n) + 3n * (8 + n)) = 0
(32 + 4n + (8 * 3n + n * 3n)) = 0
(32 + 4n + (24n + 3n2)) = 0

Combine like terms: 4n + 24n = 28n
(32 + 28n + 3n2) = 0

Solving
32 + 28n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(8 + n)(4 + 3n) = 0


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

Simplifying
8 + n = 0

Solving
8 + n = 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 + n = 0 + -8

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

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

Simplifying
n = -8

Subproblem 2
Set the factor '(4 + 3n)' equal to zero and attempt to solve:

Simplifying
4 + 3n = 0

Solving
4 + 3n = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3n = 0 + -4
3n = 0 + -4

Combine like terms: 0 + -4 = -4
3n = -4

Divide each side by '3'.
n = -1.333333333

Simplifying
n = -1.333333333
Solution
n = {-8, -1.333333333}

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