2n+n(2n)=94

Solution for 2n+n(2n)=94 equation:

Simplifying
2n + n(2n) = 94

Remove parenthesis around (2n)
2n + n * 2n = 94

Reorder the terms for easier multiplication:
2n + 2n * n = 94

Multiply n * n
2n + 2n2 = 94

Solving
2n + 2n2 = 94

Solving for variable 'n'.

Reorder the terms:
-94 + 2n + 2n2 = 94 + -94

Combine like terms: 94 + -94 = 0
-94 + 2n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-47 + n + n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-47 + n + n2)' equal to zero and attempt to solve:

Simplifying
-47 + n + n2 = 0

Solving
-47 + n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + n + 47 + n2 = 0 + 47

Reorder the terms:
-47 + 47 + n + n2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + n + n2 = 0 + 47
n + n2 = 0 + 47

Combine like terms: 0 + 47 = 47
n + n2 = 47

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.
n + 0.25 + n2 = 47 + 0.25

Reorder the terms:
0.25 + n + n2 = 47 + 0.25

Combine like terms: 47 + 0.25 = 47.25
0.25 + n + n2 = 47.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 47.25

Calculate the square root of the right side: 6.873863542

Break this problem into two subproblems by setting 
(n + 0.5) equal to 6.873863542 and -6.873863542.

Subproblem 1
n + 0.5 = 6.873863542

Simplifying
n + 0.5 = 6.873863542

Reorder the terms:
0.5 + n = 6.873863542

Solving
0.5 + n = 6.873863542

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 = 6.873863542 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 6.873863542 + -0.5
n = 6.873863542 + -0.5

Combine like terms: 6.873863542 + -0.5 = 6.373863542
n = 6.373863542

Simplifying
n = 6.373863542

Subproblem 2
n + 0.5 = -6.873863542

Simplifying
n + 0.5 = -6.873863542

Reorder the terms:
0.5 + n = -6.873863542

Solving
0.5 + n = -6.873863542

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 = -6.873863542 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -6.873863542 + -0.5
n = -6.873863542 + -0.5

Combine like terms: -6.873863542 + -0.5 = -7.373863542
n = -7.373863542

Simplifying
n = -7.373863542

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.373863542, -7.373863542}
Solution
n = {6.373863542, -7.373863542}