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

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

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

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

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

Multiply (6 + 3n) * (-3 + 6n)
(6(-3 + 6n) + 3n * (-3 + 6n)) = 0
((-3 * 6 + 6n * 6) + 3n * (-3 + 6n)) = 0
((-18 + 36n) + 3n * (-3 + 6n)) = 0
(-18 + 36n + (-3 * 3n + 6n * 3n)) = 0
(-18 + 36n + (-9n + 18n2)) = 0

Combine like terms: 36n + -9n = 27n
(-18 + 27n + 18n2) = 0

Solving
-18 + 27n + 18n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-2 + 3n + 2n2) = 0

Factor a trinomial.
9((-2 + -1n)(1 + -2n)) = 0

Ignore the factor 9.
Subproblem 1
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
Subproblem 2
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
Solution
n = {-2, 0.5}