(6n+3)(6n-4)=0

Solution for (6n+3)(6n-4)=0 equation:

Simplifying
(6n + 3)(6n + -4) = 0

Reorder the terms:
(3 + 6n)(6n + -4) = 0

Reorder the terms:
(3 + 6n)(-4 + 6n) = 0

Multiply (3 + 6n) * (-4 + 6n)
(3(-4 + 6n) + 6n * (-4 + 6n)) = 0
((-4 * 3 + 6n * 3) + 6n * (-4 + 6n)) = 0
((-12 + 18n) + 6n * (-4 + 6n)) = 0
(-12 + 18n + (-4 * 6n + 6n * 6n)) = 0
(-12 + 18n + (-24n + 36n2)) = 0

Combine like terms: 18n + -24n = -6n
(-12 + -6n + 36n2) = 0

Solving
-12 + -6n + 36n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + -1n + 6n2) = 0

Factor a trinomial.
6((-1 + -2n)(2 + -3n)) = 0

Ignore the factor 6.
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 '(2 + -3n)' equal to zero and attempt to solve:

Simplifying
2 + -3n = 0

Solving
2 + -3n = 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 + -3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3n = 0 + -2
-3n = 0 + -2

Combine like terms: 0 + -2 = -2
-3n = -2

Divide each side by '-3'.
n = 0.6666666667

Simplifying
n = 0.6666666667
Solution
n = {-0.5, 0.6666666667}