(8n-7)(n+1)=0

Solution for (8n-7)(n+1)=0 equation:

Simplifying
(8n + -7)(n + 1) = 0

Reorder the terms:
(-7 + 8n)(n + 1) = 0

Reorder the terms:
(-7 + 8n)(1 + n) = 0

Multiply (-7 + 8n) * (1 + n)
(-7(1 + n) + 8n * (1 + n)) = 0
((1 * -7 + n * -7) + 8n * (1 + n)) = 0
((-7 + -7n) + 8n * (1 + n)) = 0
(-7 + -7n + (1 * 8n + n * 8n)) = 0
(-7 + -7n + (8n + 8n2)) = 0

Combine like terms: -7n + 8n = 1n
(-7 + 1n + 8n2) = 0

Solving
-7 + 1n + 8n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -1n)(7 + -8n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -8n)' equal to zero and attempt to solve:

Simplifying
7 + -8n = 0

Solving
7 + -8n = 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 + -8n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8n = 0 + -7
-8n = 0 + -7

Combine like terms: 0 + -7 = -7
-8n = -7

Divide each side by '-8'.
n = 0.875

Simplifying
n = 0.875
Solution
n = {-1, 0.875}