6(n-7)(n-5)=0

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Solution for 6(n-7)(n-5)=0 equation: 


Simplifying
6(n + -7)(n + -5) = 0

Reorder the terms:
6(-7 + n)(n + -5) = 0

Reorder the terms:
6(-7 + n)(-5 + n) = 0

Multiply (-7 + n) * (-5 + n)
6(-7(-5 + n) + n(-5 + n)) = 0
6((-5 * -7 + n * -7) + n(-5 + n)) = 0
6((35 + -7n) + n(-5 + n)) = 0
6(35 + -7n + (-5 * n + n * n)) = 0
6(35 + -7n + (-5n + n2)) = 0

Combine like terms: -7n + -5n = -12n
6(35 + -12n + n2) = 0
(35 * 6 + -12n * 6 + n2 * 6) = 0
(210 + -72n + 6n2) = 0

Solving
210 + -72n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(35 + -12n + n2) = 0

Factor a trinomial.
6((5 + -1n)(7 + -1n)) = 0

Ignore the factor 6.

Subproblem 1
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

Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {5, 7}

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