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

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

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

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

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

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

Combine like terms: 24n + -3n = 21n
(-12 + 21n + 6n2) = 0

Solving
-12 + 21n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 7n + 2n2) = 0

Factor a trinomial.
3((-4 + -1n)(1 + -2n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
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 = {-4, 0.5}