5(n-8)(4n+5)=0

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Solution for 5(n-8)(4n+5)=0 equation: 


Simplifying
5(n + -8)(4n + 5) = 0

Reorder the terms:
5(-8 + n)(4n + 5) = 0

Reorder the terms:
5(-8 + n)(5 + 4n) = 0

Multiply (-8 + n) * (5 + 4n)
5(-8(5 + 4n) + n(5 + 4n)) = 0
5((5 * -8 + 4n * -8) + n(5 + 4n)) = 0
5((-40 + -32n) + n(5 + 4n)) = 0
5(-40 + -32n + (5 * n + 4n * n)) = 0
5(-40 + -32n + (5n + 4n2)) = 0

Combine like terms: -32n + 5n = -27n
5(-40 + -27n + 4n2) = 0
(-40 * 5 + -27n * 5 + 4n2 * 5) = 0
(-200 + -135n + 20n2) = 0

Solving
-200 + -135n + 20n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-40 + -27n + 4n2) = 0

Factor a trinomial.
5((-5 + -4n)(8 + -1n)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-5 + -4n)' equal to zero and attempt to solve:

Simplifying
-5 + -4n = 0

Solving
-5 + -4n = 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 + -4n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4n = 0 + 5
-4n = 0 + 5

Combine like terms: 0 + 5 = 5
-4n = 5

Divide each side by '-4'.
n = -1.25

Simplifying
n = -1.25

Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 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 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {-1.25, 8}

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