3(8n-7)(n+5)=0

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Solution for 3(8n-7)(n+5)=0 equation: 


Simplifying
3(8n + -7)(n + 5) = 0

Reorder the terms:
3(-7 + 8n)(n + 5) = 0

Reorder the terms:
3(-7 + 8n)(5 + n) = 0

Multiply (-7 + 8n) * (5 + n)
3(-7(5 + n) + 8n * (5 + n)) = 0
3((5 * -7 + n * -7) + 8n * (5 + n)) = 0
3((-35 + -7n) + 8n * (5 + n)) = 0
3(-35 + -7n + (5 * 8n + n * 8n)) = 0
3(-35 + -7n + (40n + 8n2)) = 0

Combine like terms: -7n + 40n = 33n
3(-35 + 33n + 8n2) = 0
(-35 * 3 + 33n * 3 + 8n2 * 3) = 0
(-105 + 99n + 24n2) = 0

Solving
-105 + 99n + 24n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-35 + 33n + 8n2) = 0

Factor a trinomial.
3((-5 + -1n)(7 + -8n)) = 0

Ignore the factor 3.

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

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 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 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5

Subproblem 2
Set the factor '(7 + -8n)' equal to zero and attempt to solve:

Simplifying
7 + -8n = 0

Solving
7 + -8n = 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 + -8n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8n = 0 + -7
-8n = 0 + -7

Combine like terms: 0 + -7 = -7
-8n = -7

Divide each side by '-8'.
n = 0.875

Simplifying
n = 0.875
Solution
n = {-5, 0.875}

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