12n(123n)(1234n)=12345n

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Solution for 12n(123n)(1234n)=12345n equation: 


Simplifying
12n(123n)(1234n) = 12345n

Remove parenthesis around (123n)
12n * 123n(1234n) = 12345n

Remove parenthesis around (1234n)
12n * 123n * 1234n = 12345n

Reorder the terms for easier multiplication:
12 * 123 * 1234n * n * n = 12345n

Multiply 12 * 123
1476 * 1234n * n * n = 12345n

Multiply 1476 * 1234
1821384n * n * n = 12345n

Multiply n * n
1821384n2 * n = 12345n

Multiply n2 * n
1821384n3 = 12345n

Solving
1821384n3 = 12345n

Solving for variable 'n'.

Reorder the terms:
-12345n + 1821384n3 = 12345n + -12345n

Combine like terms: 12345n + -12345n = 0
-12345n + 1821384n3 = 0

Factor out the Greatest Common Factor (GCF), '3n'.
3n(-4115 + 607128n2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(-4115 + 607128n2)' equal to zero and attempt to solve:

Simplifying
-4115 + 607128n2 = 0

Solving
-4115 + 607128n2 = 0

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

Add '4115' to each side of the equation.
-4115 + 4115 + 607128n2 = 0 + 4115

Combine like terms: -4115 + 4115 = 0
0 + 607128n2 = 0 + 4115
607128n2 = 0 + 4115

Combine like terms: 0 + 4115 = 4115
607128n2 = 4115

Divide each side by '607128'.
n2 = 0.006777812916

Simplifying
n2 = 0.006777812916

Take the square root of each side:
n = {-0.082327474, 0.082327474}
Solution
n = {0, -0.082327474, 0.082327474}

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