(3n-2)(n-8)=0

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Solution for (3n-2)(n-8)=0 equation: 


Simplifying
(3n + -2)(n + -8) = 0

Reorder the terms:
(-2 + 3n)(n + -8) = 0

Reorder the terms:
(-2 + 3n)(-8 + n) = 0

Multiply (-2 + 3n) * (-8 + n)
(-2(-8 + n) + 3n * (-8 + n)) = 0
((-8 * -2 + n * -2) + 3n * (-8 + n)) = 0
((16 + -2n) + 3n * (-8 + n)) = 0
(16 + -2n + (-8 * 3n + n * 3n)) = 0
(16 + -2n + (-24n + 3n2)) = 0

Combine like terms: -2n + -24n = -26n
(16 + -26n + 3n2) = 0

Solving
16 + -26n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(2 + -3n)(8 + -1n) = 0


Subproblem 1
Set the factor '(2 + -3n)' equal to zero and attempt to solve:

Simplifying
2 + -3n = 0

Solving
2 + -3n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3n = 0 + -2
-3n = 0 + -2

Combine like terms: 0 + -2 = -2
-3n = -2

Divide each side by '-3'.
n = 0.6666666667

Simplifying
n = 0.6666666667

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 = {0.6666666667, 8}

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