(n+6)(2n-5)=55

Solution for (n+6)(2n-5)=55 equation:

Simplifying
(n + 6)(2n + -5) = 55

Reorder the terms:
(6 + n)(2n + -5) = 55

Reorder the terms:
(6 + n)(-5 + 2n) = 55

Multiply (6 + n) * (-5 + 2n)
(6(-5 + 2n) + n(-5 + 2n)) = 55
((-5 * 6 + 2n * 6) + n(-5 + 2n)) = 55
((-30 + 12n) + n(-5 + 2n)) = 55
(-30 + 12n + (-5 * n + 2n * n)) = 55
(-30 + 12n + (-5n + 2n2)) = 55

Combine like terms: 12n + -5n = 7n
(-30 + 7n + 2n2) = 55

Solving
-30 + 7n + 2n2 = 55

Solving for variable 'n'.

Reorder the terms:
-30 + -55 + 7n + 2n2 = 55 + -55

Combine like terms: -30 + -55 = -85
-85 + 7n + 2n2 = 55 + -55

Combine like terms: 55 + -55 = 0
-85 + 7n + 2n2 = 0

Factor a trinomial.
(-17 + -2n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-17 + -2n)' equal to zero and attempt to solve:

Simplifying
-17 + -2n = 0

Solving
-17 + -2n = 0

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

Add '17' to each side of the equation.
-17 + 17 + -2n = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -2n = 0 + 17
-2n = 0 + 17

Combine like terms: 0 + 17 = 17
-2n = 17

Divide each side by '-2'.
n = -8.5

Simplifying
n = -8.5
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-8.5, 5}