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

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

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

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

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

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

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

Solving
-8 + -1n + 7n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -1n)(8 + -7n) = 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 '(8 + -7n)' equal to zero and attempt to solve:

Simplifying
8 + -7n = 0

Solving
8 + -7n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7n = 0 + -8

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

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

Divide each side by '-7'.
n = 1.142857143

Simplifying
n = 1.142857143
Solution
n = {-1, 1.142857143}