(3n-4)(n+1)=0

Solution for (3n-4)(n+1)=0 equation:

Simplifying
(3n + -4)(n + 1) = 0

Reorder the terms:
(-4 + 3n)(n + 1) = 0

Reorder the terms:
(-4 + 3n)(1 + n) = 0

Multiply (-4 + 3n) * (1 + n)
(-4(1 + n) + 3n * (1 + n)) = 0
((1 * -4 + n * -4) + 3n * (1 + n)) = 0
((-4 + -4n) + 3n * (1 + n)) = 0
(-4 + -4n + (1 * 3n + n * 3n)) = 0
(-4 + -4n + (3n + 3n2)) = 0

Combine like terms: -4n + 3n = -1n
(-4 + -1n + 3n2) = 0

Solving
-4 + -1n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -1n)(4 + -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 '(4 + -3n)' equal to zero and attempt to solve:

Simplifying
4 + -3n = 0

Solving
4 + -3n = 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 + -3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3n = 0 + -4
-3n = 0 + -4

Combine like terms: 0 + -4 = -4
-3n = -4

Divide each side by '-3'.
n = 1.333333333

Simplifying
n = 1.333333333
Solution
n = {-1, 1.333333333}