(n+3)(6n-1)=0

Solution for (n+3)(6n-1)=0 equation:

Simplifying
(n + 3)(6n + -1) = 0

Reorder the terms:
(3 + n)(6n + -1) = 0

Reorder the terms:
(3 + n)(-1 + 6n) = 0

Multiply (3 + n) * (-1 + 6n)
(3(-1 + 6n) + n(-1 + 6n)) = 0
((-1 * 3 + 6n * 3) + n(-1 + 6n)) = 0
((-3 + 18n) + n(-1 + 6n)) = 0
(-3 + 18n + (-1 * n + 6n * n)) = 0
(-3 + 18n + (-1n + 6n2)) = 0

Combine like terms: 18n + -1n = 17n
(-3 + 17n + 6n2) = 0

Solving
-3 + 17n + 6n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-3 + -1n)(1 + -6n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -6n)' equal to zero and attempt to solve:

Simplifying
1 + -6n = 0

Solving
1 + -6n = 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 + -6n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6n = 0 + -1
-6n = 0 + -1

Combine like terms: 0 + -1 = -1
-6n = -1

Divide each side by '-6'.
n = 0.1666666667

Simplifying
n = 0.1666666667
Solution
n = {-3, 0.1666666667}