8(6n+5)(n+5)=0

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Solution for 8(6n+5)(n+5)=0 equation: 


Simplifying
8(6n + 5)(n + 5) = 0

Reorder the terms:
8(5 + 6n)(n + 5) = 0

Reorder the terms:
8(5 + 6n)(5 + n) = 0

Multiply (5 + 6n) * (5 + n)
8(5(5 + n) + 6n * (5 + n)) = 0
8((5 * 5 + n * 5) + 6n * (5 + n)) = 0
8((25 + 5n) + 6n * (5 + n)) = 0
8(25 + 5n + (5 * 6n + n * 6n)) = 0
8(25 + 5n + (30n + 6n2)) = 0

Combine like terms: 5n + 30n = 35n
8(25 + 35n + 6n2) = 0
(25 * 8 + 35n * 8 + 6n2 * 8) = 0
(200 + 280n + 48n2) = 0

Solving
200 + 280n + 48n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '8'.
8(25 + 35n + 6n2) = 0

Factor a trinomial.
8((5 + n)(5 + 6n)) = 0

Ignore the factor 8.

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

Simplifying
5 + n = 0

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

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

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

Simplifying
n = -5

Subproblem 2
Set the factor '(5 + 6n)' equal to zero and attempt to solve:

Simplifying
5 + 6n = 0

Solving
5 + 6n = 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 + 6n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6n = 0 + -5
6n = 0 + -5

Combine like terms: 0 + -5 = -5
6n = -5

Divide each side by '6'.
n = -0.8333333333

Simplifying
n = -0.8333333333
Solution
n = {-5, -0.8333333333}

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