(6+n)(1-n)=10

Solution for (6+n)(1-n)=10 equation:

Simplifying
(6 + n)(1 + -1n) = 10

Multiply (6 + n) * (1 + -1n)
(6(1 + -1n) + n(1 + -1n)) = 10
((1 * 6 + -1n * 6) + n(1 + -1n)) = 10
((6 + -6n) + n(1 + -1n)) = 10
(6 + -6n + (1 * n + -1n * n)) = 10
(6 + -6n + (1n + -1n2)) = 10

Combine like terms: -6n + 1n = -5n
(6 + -5n + -1n2) = 10

Solving
6 + -5n + -1n2 = 10

Solving for variable 'n'.

Reorder the terms:
6 + -10 + -5n + -1n2 = 10 + -10

Combine like terms: 6 + -10 = -4
-4 + -5n + -1n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-4 + -5n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 5n + n2) = 0

Factor a trinomial.
-1((4 + n)(1 + n)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

Simplifying
n = -1
Solution
n = {-4, -1}