(2n-14)(n-5)=90

Solution for (2n-14)(n-5)=90 equation:

Simplifying
(2n + -14)(n + -5) = 90

Reorder the terms:
(-14 + 2n)(n + -5) = 90

Reorder the terms:
(-14 + 2n)(-5 + n) = 90

Multiply (-14 + 2n) * (-5 + n)
(-14(-5 + n) + 2n * (-5 + n)) = 90
((-5 * -14 + n * -14) + 2n * (-5 + n)) = 90
((70 + -14n) + 2n * (-5 + n)) = 90
(70 + -14n + (-5 * 2n + n * 2n)) = 90
(70 + -14n + (-10n + 2n2)) = 90

Combine like terms: -14n + -10n = -24n
(70 + -24n + 2n2) = 90

Solving
70 + -24n + 2n2 = 90

Solving for variable 'n'.

Reorder the terms:
70 + -90 + -24n + 2n2 = 90 + -90

Combine like terms: 70 + -90 = -20
-20 + -24n + 2n2 = 90 + -90

Combine like terms: 90 + -90 = 0
-20 + -24n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -12n + n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -12n + n2)' equal to zero and attempt to solve:

Simplifying
-10 + -12n + n2 = 0

Solving
-10 + -12n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -12n + 10 + n2 = 0 + 10

Reorder the terms:
-10 + 10 + -12n + n2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -12n + n2 = 0 + 10
-12n + n2 = 0 + 10

Combine like terms: 0 + 10 = 10
-12n + n2 = 10

The n term is -12n.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12n + 36 + n2 = 10 + 36

Reorder the terms:
36 + -12n + n2 = 10 + 36

Combine like terms: 10 + 36 = 46
36 + -12n + n2 = 46

Factor a perfect square on the left side:
(n + -6)(n + -6) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(n + -6) equal to 6.782329983 and -6.782329983.

Subproblem 1
n + -6 = 6.782329983

Simplifying
n + -6 = 6.782329983

Reorder the terms:
-6 + n = 6.782329983

Solving
-6 + n = 6.782329983

Solving for variable 'n'.

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

Add '6' to each side of the equation.
-6 + 6 + n = 6.782329983 + 6

Combine like terms: -6 + 6 = 0
0 + n = 6.782329983 + 6
n = 6.782329983 + 6

Combine like terms: 6.782329983 + 6 = 12.782329983
n = 12.782329983

Simplifying
n = 12.782329983

Subproblem 2
n + -6 = -6.782329983

Simplifying
n + -6 = -6.782329983

Reorder the terms:
-6 + n = -6.782329983

Solving
-6 + n = -6.782329983

Solving for variable 'n'.

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

Add '6' to each side of the equation.
-6 + 6 + n = -6.782329983 + 6

Combine like terms: -6 + 6 = 0
0 + n = -6.782329983 + 6
n = -6.782329983 + 6

Combine like terms: -6.782329983 + 6 = -0.782329983
n = -0.782329983

Simplifying
n = -0.782329983

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {12.782329983, -0.782329983}
Solution
n = {12.782329983, -0.782329983}