(n+9)(2n-4)=90

Solution for (n+9)(2n-4)=90 equation:

Simplifying
(n + 9)(2n + -4) = 90

Reorder the terms:
(9 + n)(2n + -4) = 90

Reorder the terms:
(9 + n)(-4 + 2n) = 90

Multiply (9 + n) * (-4 + 2n)
(9(-4 + 2n) + n(-4 + 2n)) = 90
((-4 * 9 + 2n * 9) + n(-4 + 2n)) = 90
((-36 + 18n) + n(-4 + 2n)) = 90
(-36 + 18n + (-4 * n + 2n * n)) = 90
(-36 + 18n + (-4n + 2n2)) = 90

Combine like terms: 18n + -4n = 14n
(-36 + 14n + 2n2) = 90

Solving
-36 + 14n + 2n2 = 90

Solving for variable 'n'.

Reorder the terms:
-36 + -90 + 14n + 2n2 = 90 + -90

Combine like terms: -36 + -90 = -126
-126 + 14n + 2n2 = 90 + -90

Combine like terms: 90 + -90 = 0
-126 + 14n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-63 + 7n + n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-63 + 7n + n2)' equal to zero and attempt to solve:

Simplifying
-63 + 7n + n2 = 0

Solving
-63 + 7n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '63' to each side of the equation.
-63 + 7n + 63 + n2 = 0 + 63

Reorder the terms:
-63 + 63 + 7n + n2 = 0 + 63

Combine like terms: -63 + 63 = 0
0 + 7n + n2 = 0 + 63
7n + n2 = 0 + 63

Combine like terms: 0 + 63 = 63
7n + n2 = 63

The n term is 7n.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7n + 12.25 + n2 = 63 + 12.25

Reorder the terms:
12.25 + 7n + n2 = 63 + 12.25

Combine like terms: 63 + 12.25 = 75.25
12.25 + 7n + n2 = 75.25

Factor a perfect square on the left side:
(n + 3.5)(n + 3.5) = 75.25

Calculate the square root of the right side: 8.674675786

Break this problem into two subproblems by setting 
(n + 3.5) equal to 8.674675786 and -8.674675786.

Subproblem 1
n + 3.5 = 8.674675786

Simplifying
n + 3.5 = 8.674675786

Reorder the terms:
3.5 + n = 8.674675786

Solving
3.5 + n = 8.674675786

Solving for variable 'n'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + n = 8.674675786 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + n = 8.674675786 + -3.5
n = 8.674675786 + -3.5

Combine like terms: 8.674675786 + -3.5 = 5.174675786
n = 5.174675786

Simplifying
n = 5.174675786

Subproblem 2
n + 3.5 = -8.674675786

Simplifying
n + 3.5 = -8.674675786

Reorder the terms:
3.5 + n = -8.674675786

Solving
3.5 + n = -8.674675786

Solving for variable 'n'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + n = -8.674675786 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + n = -8.674675786 + -3.5
n = -8.674675786 + -3.5

Combine like terms: -8.674675786 + -3.5 = -12.174675786
n = -12.174675786

Simplifying
n = -12.174675786

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {5.174675786, -12.174675786}
Solution
n = {5.174675786, -12.174675786}