(2n-6)(10n-5)=0

Solution for (2n-6)(10n-5)=0 equation:

Simplifying
(2n + -6)(10n + -5) = 0

Reorder the terms:
(-6 + 2n)(10n + -5) = 0

Reorder the terms:
(-6 + 2n)(-5 + 10n) = 0

Multiply (-6 + 2n) * (-5 + 10n)
(-6(-5 + 10n) + 2n * (-5 + 10n)) = 0
((-5 * -6 + 10n * -6) + 2n * (-5 + 10n)) = 0
((30 + -60n) + 2n * (-5 + 10n)) = 0
(30 + -60n + (-5 * 2n + 10n * 2n)) = 0
(30 + -60n + (-10n + 20n2)) = 0

Combine like terms: -60n + -10n = -70n
(30 + -70n + 20n2) = 0

Solving
30 + -70n + 20n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '10'.
10(3 + -7n + 2n2) = 0

Factor a trinomial.
10((1 + -2n)(3 + -1n)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(1 + -2n)' equal to zero and attempt to solve:

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
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 = {0.5, 3}