(2n)(11n-14)=90

Solution for (2n)(11n-14)=90 equation:

Simplifying
(2n)(11n + -14) = 90

Remove parenthesis around (2n)
2n(11n + -14) = 90

Reorder the terms:
2n(-14 + 11n) = 90
(-14 * 2n + 11n * 2n) = 90
(-28n + 22n2) = 90

Solving
-28n + 22n2 = 90

Solving for variable 'n'.

Reorder the terms:
-90 + -28n + 22n2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -28n + 22n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -14n + 11n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-45 + -14n + 11n2)' equal to zero and attempt to solve:

Simplifying
-45 + -14n + 11n2 = 0

Solving
-45 + -14n + 11n2 = 0

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

Divide each side by '11'.
-4.090909091 + -1.272727273n + n2 = 0

Move the constant term to the right:

Add '4.090909091' to each side of the equation.
-4.090909091 + -1.272727273n + 4.090909091 + n2 = 0 + 4.090909091

Reorder the terms:
-4.090909091 + 4.090909091 + -1.272727273n + n2 = 0 + 4.090909091

Combine like terms: -4.090909091 + 4.090909091 = 0.000000000
0.000000000 + -1.272727273n + n2 = 0 + 4.090909091
-1.272727273n + n2 = 0 + 4.090909091

Combine like terms: 0 + 4.090909091 = 4.090909091
-1.272727273n + n2 = 4.090909091

The n term is -1.272727273n.  Take half its coefficient (-0.6363636365).
Square it (0.4049586779) and add it to both sides.

Add '0.4049586779' to each side of the equation.
-1.272727273n + 0.4049586779 + n2 = 4.090909091 + 0.4049586779

Reorder the terms:
0.4049586779 + -1.272727273n + n2 = 4.090909091 + 0.4049586779

Combine like terms: 4.090909091 + 0.4049586779 = 4.4958677689
0.4049586779 + -1.272727273n + n2 = 4.4958677689

Factor a perfect square on the left side:
(n + -0.6363636365)(n + -0.6363636365) = 4.4958677689

Calculate the square root of the right side: 2.120346144

Break this problem into two subproblems by setting 
(n + -0.6363636365) equal to 2.120346144 and -2.120346144.

Subproblem 1
n + -0.6363636365 = 2.120346144

Simplifying
n + -0.6363636365 = 2.120346144

Reorder the terms:
-0.6363636365 + n = 2.120346144

Solving
-0.6363636365 + n = 2.120346144

Solving for variable 'n'.

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

Add '0.6363636365' to each side of the equation.
-0.6363636365 + 0.6363636365 + n = 2.120346144 + 0.6363636365

Combine like terms: -0.6363636365 + 0.6363636365 = 0.0000000000
0.0000000000 + n = 2.120346144 + 0.6363636365
n = 2.120346144 + 0.6363636365

Combine like terms: 2.120346144 + 0.6363636365 = 2.7567097805
n = 2.7567097805

Simplifying
n = 2.7567097805

Subproblem 2
n + -0.6363636365 = -2.120346144

Simplifying
n + -0.6363636365 = -2.120346144

Reorder the terms:
-0.6363636365 + n = -2.120346144

Solving
-0.6363636365 + n = -2.120346144

Solving for variable 'n'.

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

Add '0.6363636365' to each side of the equation.
-0.6363636365 + 0.6363636365 + n = -2.120346144 + 0.6363636365

Combine like terms: -0.6363636365 + 0.6363636365 = 0.0000000000
0.0000000000 + n = -2.120346144 + 0.6363636365
n = -2.120346144 + 0.6363636365

Combine like terms: -2.120346144 + 0.6363636365 = -1.4839825075
n = -1.4839825075

Simplifying
n = -1.4839825075

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.7567097805, -1.4839825075}
Solution
n = {2.7567097805, -1.4839825075}