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

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

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

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

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

Multiply (-1 + 3n) * (4 + n)
(-1(4 + n) + 3n * (4 + n)) = 0solven
((4 * -1 + n * -1) + 3n * (4 + n)) = 0solven
((-4 + -1n) + 3n * (4 + n)) = 0solven
(-4 + -1n + (4 * 3n + n * 3n)) = 0solven
(-4 + -1n + (12n + 3n2)) = 0solven

Combine like terms: -1n + 12n = 11n
(-4 + 11n + 3n2) = 0solven

Anything times zero is zero.
-4 + 11n + 3n2 = 0elnosv

Solving
-4 + 11n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-4 + -1n)(1 + -3n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

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

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve:

Simplifying
1 + -3n = 0

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

Combine like terms: 1 + -1 = 0
0 + -3n = 0 + -1
-3n = 0 + -1

Combine like terms: 0 + -1 = -1
-3n = -1

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Solution
n = {-4, 0.3333333333}