3+3n(1+8n)=

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Solution for 3+3n(1+8n)= equation: 


Simplifying
3 + 3n(1 + 8n) = 0
3 + (1 * 3n + 8n * 3n) = 0
3 + (3n + 24n2) = 0

Solving
3 + 3n + 24n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + n + 8n2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(1 + n + 8n2)' equal to zero and attempt to solve:

Simplifying
1 + n + 8n2 = 0

Solving
1 + n + 8n2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
0.125 + 0.125n + n2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 0.125n + -0.125 + n2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 0.125n + n2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 0.125n + n2 = 0 + -0.125
0.125n + n2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
0.125n + n2 = -0.125

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.125n + 0.25 + n2 = -0.125 + 0.25

Reorder the terms:
0.25 + 0.125n + n2 = -0.125 + 0.25

Combine like terms: -0.125 + 0.25 = 0.125
0.25 + 0.125n + n2 = 0.125

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 0.125

Calculate the square root of the right side: 0.353553391

Break this problem into two subproblems by setting 
(n + 0.5) equal to 0.353553391 and -0.353553391.


Subproblem 1
n + 0.5 = 0.353553391

Simplifying
n + 0.5 = 0.353553391

Reorder the terms:
0.5 + n = 0.353553391

Solving
0.5 + n = 0.353553391

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = 0.353553391 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 0.353553391 + -0.5
n = 0.353553391 + -0.5

Combine like terms: 0.353553391 + -0.5 = -0.146446609
n = -0.146446609

Simplifying
n = -0.146446609


Subproblem 2
n + 0.5 = -0.353553391

Simplifying
n + 0.5 = -0.353553391

Reorder the terms:
0.5 + n = -0.353553391

Solving
0.5 + n = -0.353553391

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = -0.353553391 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -0.353553391 + -0.5
n = -0.353553391 + -0.5

Combine like terms: -0.353553391 + -0.5 = -0.853553391
n = -0.853553391

Simplifying
n = -0.853553391


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.146446609, -0.853553391}
Solution
n = {-0.146446609, -0.853553391}

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