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

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

Simplifying
(2n + -14)(5 + n) = 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 = -4n
(-70 + -4n + 2n2) = 90

Solving
-70 + -4n + 2n2 = 90

Solving for variable 'n'.

Reorder the terms:
-70 + -90 + -4n + 2n2 = 90 + -90

Combine like terms: -70 + -90 = -160
-160 + -4n + 2n2 = 90 + -90

Combine like terms: 90 + -90 = 0
-160 + -4n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-80 + -2n + n2) = 0

Factor a trinomial.
2((-8 + -1n)(10 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Solution
n = {-8, 10}