(n+6)(4n-1)=0

Solution for (n+6)(4n-1)=0 equation:

Simplifying
(n + 6)(4n + -1) = 0

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

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

Multiply (6 + n) * (-1 + 4n)
(6(-1 + 4n) + n(-1 + 4n)) = 0
((-1 * 6 + 4n * 6) + n(-1 + 4n)) = 0
((-6 + 24n) + n(-1 + 4n)) = 0
(-6 + 24n + (-1 * n + 4n * n)) = 0
(-6 + 24n + (-1n + 4n2)) = 0

Combine like terms: 24n + -1n = 23n
(-6 + 23n + 4n2) = 0

Solving
-6 + 23n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-6 + -1n)(1 + -4n) = 0

Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(1 + -4n)' equal to zero and attempt to solve:

Simplifying
1 + -4n = 0

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

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

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

Divide each side by '-4'.
n = 0.25

Simplifying
n = 0.25
Solution
n = {-6, 0.25}