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

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


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

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

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

Multiply (-2 + n) * (-8 + 3n)
(-2(-8 + 3n) + n(-8 + 3n)) = 0
((-8 * -2 + 3n * -2) + n(-8 + 3n)) = 0
((16 + -6n) + n(-8 + 3n)) = 0
(16 + -6n + (-8 * n + 3n * n)) = 0
(16 + -6n + (-8n + 3n2)) = 0

Combine like terms: -6n + -8n = -14n
(16 + -14n + 3n2) = 0

Solving
16 + -14n + 3n2 = 0

Solving for variable 'n'.

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


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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2

Subproblem 2
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
Solution
n = {2, 2.666666667}

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