(n-4)(7n-1)=0

Solution for (n-4)(7n-1)=0 equation:

Simplifying
(n + -4)(7n + -1) = 0

Reorder the terms:
(-4 + n)(7n + -1) = 0

Reorder the terms:
(-4 + n)(-1 + 7n) = 0

Multiply (-4 + n) * (-1 + 7n)
(-4(-1 + 7n) + n(-1 + 7n)) = 0
((-1 * -4 + 7n * -4) + n(-1 + 7n)) = 0
((4 + -28n) + n(-1 + 7n)) = 0
(4 + -28n + (-1 * n + 7n * n)) = 0
(4 + -28n + (-1n + 7n2)) = 0

Combine like terms: -28n + -1n = -29n
(4 + -29n + 7n2) = 0

Solving
4 + -29n + 7n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + -7n)(4 + -1n) = 0

Subproblem 1
Set the factor '(1 + -7n)' equal to zero and attempt to solve:

Simplifying
1 + -7n = 0

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

Combine like terms: 1 + -1 = 0
0 + -7n = 0 + -1
-7n = 0 + -1

Combine like terms: 0 + -1 = -1
-7n = -1

Divide each side by '-7'.
n = 0.1428571429

Simplifying
n = 0.1428571429
Subproblem 2
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
Solution
n = {0.1428571429, 4}