(-6n+2)(5n+3)=0

Solution for (-6n+2)(5n+3)=0 equation:

Simplifying
(-6n + 2)(5n + 3) = 0

Reorder the terms:
(2 + -6n)(5n + 3) = 0

Reorder the terms:
(2 + -6n)(3 + 5n) = 0

Multiply (2 + -6n) * (3 + 5n)
(2(3 + 5n) + -6n * (3 + 5n)) = 0
((3 * 2 + 5n * 2) + -6n * (3 + 5n)) = 0
((6 + 10n) + -6n * (3 + 5n)) = 0
(6 + 10n + (3 * -6n + 5n * -6n)) = 0
(6 + 10n + (-18n + -30n2)) = 0

Combine like terms: 10n + -18n = -8n
(6 + -8n + -30n2) = 0

Solving
6 + -8n + -30n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -4n + -15n2) = 0

Factor a trinomial.
2((1 + -3n)(3 + 5n)) = 0

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

Simplifying
1 + -3n = 0

Solving
1 + -3n = 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 + -3n = 0 + -1

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

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

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Subproblem 2
Set the factor '(3 + 5n)' equal to zero and attempt to solve:

Simplifying
3 + 5n = 0

Solving
3 + 5n = 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 + 5n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5n = 0 + -3
5n = 0 + -3

Combine like terms: 0 + -3 = -3
5n = -3

Divide each side by '5'.
n = -0.6

Simplifying
n = -0.6
Solution
n = {0.3333333333, -0.6}