4n(6n+2)+n(3n+7)=

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Solution for 4n(6n+2)+n(3n+7)= equation: 


Simplifying
4n(6n + 2) + n(3n + 7) = 0

Reorder the terms:
4n(2 + 6n) + n(3n + 7) = 0
(2 * 4n + 6n * 4n) + n(3n + 7) = 0
(8n + 24n2) + n(3n + 7) = 0

Reorder the terms:
8n + 24n2 + n(7 + 3n) = 0
8n + 24n2 + (7 * n + 3n * n) = 0
8n + 24n2 + (7n + 3n2) = 0

Reorder the terms:
8n + 7n + 24n2 + 3n2 = 0

Combine like terms: 8n + 7n = 15n
15n + 24n2 + 3n2 = 0

Combine like terms: 24n2 + 3n2 = 27n2
15n + 27n2 = 0

Solving
15n + 27n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3n'.
3n(5 + 9n) = 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 '(5 + 9n)' equal to zero and attempt to solve:

Simplifying
5 + 9n = 0

Solving
5 + 9n = 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 + 9n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 9n = 0 + -5
9n = 0 + -5

Combine like terms: 0 + -5 = -5
9n = -5

Divide each side by '9'.
n = -0.5555555556

Simplifying
n = -0.5555555556
Solution
n = {0, -0.5555555556}

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