(n-1)(n+7)=

Solution for (n-1)(n+7)= equation:

Simplifying
(n + -1)(n + 7) = 0

Reorder the terms:
(-1 + n)(n + 7) = 0

Reorder the terms:
(-1 + n)(7 + n) = 0

Multiply (-1 + n) * (7 + n)
(-1(7 + n) + n(7 + n)) = 0
((7 * -1 + n * -1) + n(7 + n)) = 0
((-7 + -1n) + n(7 + n)) = 0
(-7 + -1n + (7 * n + n * n)) = 0
(-7 + -1n + (7n + n2)) = 0

Combine like terms: -1n + 7n = 6n
(-7 + 6n + n2) = 0

Solving
-7 + 6n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-7 + -1n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 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 + -1n = 0 + -1

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

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

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

Simplifying
n = 1
Solution
n = {-7, 1}