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

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

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

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

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

Multiply (-6 + 3n) * (2 + 5n)
(-6(2 + 5n) + 3n * (2 + 5n)) = 0
((2 * -6 + 5n * -6) + 3n * (2 + 5n)) = 0
((-12 + -30n) + 3n * (2 + 5n)) = 0
(-12 + -30n + (2 * 3n + 5n * 3n)) = 0
(-12 + -30n + (6n + 15n2)) = 0

Combine like terms: -30n + 6n = -24n
(-12 + -24n + 15n2) = 0

Solving
-12 + -24n + 15n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -8n + 5n2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -5n)' equal to zero and attempt to solve:

Simplifying
-2 + -5n = 0

Solving
-2 + -5n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5n = 0 + 2
-5n = 0 + 2

Combine like terms: 0 + 2 = 2
-5n = 2

Divide each side by '-5'.
n = -0.4

Simplifying
n = -0.4
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

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

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

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-0.4, 2}