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

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


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

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

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

Multiply (-5 + n) * (-8 + 3n)
(-5(-8 + 3n) + n(-8 + 3n)) = 0
((-8 * -5 + 3n * -5) + n(-8 + 3n)) = 0
((40 + -15n) + n(-8 + 3n)) = 0
(40 + -15n + (-8 * n + 3n * n)) = 0
(40 + -15n + (-8n + 3n2)) = 0

Combine like terms: -15n + -8n = -23n
(40 + -23n + 3n2) = 0

Solving
40 + -23n + 3n2 = 0

Solving for variable 'n'.

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


Subproblem 1
Set the factor '(8 + -3n)' equal to zero and attempt to solve:

Simplifying
8 + -3n = 0

Solving
8 + -3n = 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 + -3n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3n = 0 + -8
-3n = 0 + -8

Combine like terms: 0 + -8 = -8
-3n = -8

Divide each side by '-3'.
n = 2.666666667

Simplifying
n = 2.666666667

Subproblem 2
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
Solution
n = {2.666666667, 5}

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