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

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

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

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

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

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

Combine like terms: 3n + 24n = 27n
(18 + 27n + 4n2) = 0

Solving
18 + 27n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(6 + n)(3 + 4n) = 0

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

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

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

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

Simplifying
n = -6
Subproblem 2
Set the factor '(3 + 4n)' equal to zero and attempt to solve:

Simplifying
3 + 4n = 0

Solving
3 + 4n = 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 + 4n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4n = 0 + -3
4n = 0 + -3

Combine like terms: 0 + -3 = -3
4n = -3

Divide each side by '4'.
n = -0.75

Simplifying
n = -0.75
Solution
n = {-6, -0.75}