(12n-4)*(n+8)=0

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Solution for (12n-4)*(n+8)=0 equation: 


Simplifying
(12n + -4)(n + 8) = 0

Reorder the terms:
(-4 + 12n)(n + 8) = 0

Reorder the terms:
(-4 + 12n)(8 + n) = 0

Multiply (-4 + 12n) * (8 + n)
(-4(8 + n) + 12n * (8 + n)) = 0
((8 * -4 + n * -4) + 12n * (8 + n)) = 0
((-32 + -4n) + 12n * (8 + n)) = 0
(-32 + -4n + (8 * 12n + n * 12n)) = 0
(-32 + -4n + (96n + 12n2)) = 0

Combine like terms: -4n + 96n = 92n
(-32 + 92n + 12n2) = 0

Solving
-32 + 92n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + 23n + 3n2) = 0

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

Ignore the factor 4.

Subproblem 1
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

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

Simplifying
1 + -3n = 0

Solving
1 + -3n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3n = 0 + -1
-3n = 0 + -1

Combine like terms: 0 + -1 = -1
-3n = -1

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Solution
n = {-8, 0.3333333333}

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