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

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

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

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

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

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

Combine like terms: -12n + -1n = -13n
(3 + -13n + 4n2) = 0

Solving
3 + -13n + 4n2 = 0

Solving for variable 'n'.

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

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

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

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

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

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {0.25, 3}