(3n-11)(n+1)=0

Solution for (3n-11)(n+1)=0 equation:

Simplifying
(3n + -11)(n + 1) = 0

Reorder the terms:
(-11 + 3n)(n + 1) = 0

Reorder the terms:
(-11 + 3n)(1 + n) = 0

Multiply (-11 + 3n) * (1 + n)
(-11(1 + n) + 3n * (1 + n)) = 0
((1 * -11 + n * -11) + 3n * (1 + n)) = 0
((-11 + -11n) + 3n * (1 + n)) = 0
(-11 + -11n + (1 * 3n + n * 3n)) = 0
(-11 + -11n + (3n + 3n2)) = 0

Combine like terms: -11n + 3n = -8n
(-11 + -8n + 3n2) = 0

Solving
-11 + -8n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -1n)(11 + -3n) = 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 '(11 + -3n)' equal to zero and attempt to solve:

Simplifying
11 + -3n = 0

Solving
11 + -3n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3n = 0 + -11
-3n = 0 + -11

Combine like terms: 0 + -11 = -11
-3n = -11

Divide each side by '-3'.
n = 3.666666667

Simplifying
n = 3.666666667
Solution
n = {-1, 3.666666667}