(n-3)(8n-2)=0

Solution for (n-3)(8n-2)=0 equation:

Simplifying
(n + -3)(8n + -2) = 0

Reorder the terms:
(-3 + n)(8n + -2) = 0

Reorder the terms:
(-3 + n)(-2 + 8n) = 0

Multiply (-3 + n) * (-2 + 8n)
(-3(-2 + 8n) + n(-2 + 8n)) = 0
((-2 * -3 + 8n * -3) + n(-2 + 8n)) = 0
((6 + -24n) + n(-2 + 8n)) = 0
(6 + -24n + (-2 * n + 8n * n)) = 0
(6 + -24n + (-2n + 8n2)) = 0

Combine like terms: -24n + -2n = -26n
(6 + -26n + 8n2) = 0

Solving
6 + -26n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -13n + 4n2) = 0

Factor a trinomial.
2((1 + -4n)(3 + -1n)) = 0

Ignore the factor 2.
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}