(n+5)(n-4)=10

Solution for (n+5)(n-4)=10 equation:

Simplifying
(n + 5)(n + -4) = 10

Reorder the terms:
(5 + n)(n + -4) = 10

Reorder the terms:
(5 + n)(-4 + n) = 10

Multiply (5 + n) * (-4 + n)
(5(-4 + n) + n(-4 + n)) = 10
((-4 * 5 + n * 5) + n(-4 + n)) = 10
((-20 + 5n) + n(-4 + n)) = 10
(-20 + 5n + (-4 * n + n * n)) = 10
(-20 + 5n + (-4n + n2)) = 10

Combine like terms: 5n + -4n = 1n
(-20 + 1n + n2) = 10

Solving
-20 + 1n + n2 = 10

Solving for variable 'n'.

Reorder the terms:
-20 + -10 + 1n + n2 = 10 + -10

Combine like terms: -20 + -10 = -30
-30 + 1n + n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-30 + 1n + n2 = 0

Factor a trinomial.
(-6 + -1n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
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 = {-6, 5}