3(n-8)(3n-4)=0

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Solution for 3(n-8)(3n-4)=0 equation: 


Simplifying
3(n + -8)(3n + -4) = 0

Reorder the terms:
3(-8 + n)(3n + -4) = 0

Reorder the terms:
3(-8 + n)(-4 + 3n) = 0

Multiply (-8 + n) * (-4 + 3n)
3(-8(-4 + 3n) + n(-4 + 3n)) = 0
3((-4 * -8 + 3n * -8) + n(-4 + 3n)) = 0
3((32 + -24n) + n(-4 + 3n)) = 0
3(32 + -24n + (-4 * n + 3n * n)) = 0
3(32 + -24n + (-4n + 3n2)) = 0

Combine like terms: -24n + -4n = -28n
3(32 + -28n + 3n2) = 0
(32 * 3 + -28n * 3 + 3n2 * 3) = 0
(96 + -84n + 9n2) = 0

Solving
96 + -84n + 9n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(32 + -28n + 3n2) = 0

Factor a trinomial.
3((4 + -3n)(8 + -1n)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(4 + -3n)' equal to zero and attempt to solve:

Simplifying
4 + -3n = 0

Solving
4 + -3n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3n = 0 + -4
-3n = 0 + -4

Combine like terms: 0 + -4 = -4
-3n = -4

Divide each side by '-3'.
n = 1.333333333

Simplifying
n = 1.333333333

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 = {1.333333333, 8}

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