(8n+3)(4n+2)=

Solution for (8n+3)(4n+2)= equation:

Simplifying
(8n + 3)(4n + 2) = 0

Reorder the terms:
(3 + 8n)(4n + 2) = 0

Reorder the terms:
(3 + 8n)(2 + 4n) = 0

Multiply (3 + 8n) * (2 + 4n)
(3(2 + 4n) + 8n * (2 + 4n)) = 0
((2 * 3 + 4n * 3) + 8n * (2 + 4n)) = 0
((6 + 12n) + 8n * (2 + 4n)) = 0
(6 + 12n + (2 * 8n + 4n * 8n)) = 0
(6 + 12n + (16n + 32n2)) = 0

Combine like terms: 12n + 16n = 28n
(6 + 28n + 32n2) = 0

Solving
6 + 28n + 32n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 14n + 16n2) = 0

Factor a trinomial.
2((1 + 2n)(3 + 8n)) = 0

Ignore the factor 2.
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 '(3 + 8n)' equal to zero and attempt to solve:

Simplifying
3 + 8n = 0

Solving
3 + 8n = 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 + 8n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8n = 0 + -3
8n = 0 + -3

Combine like terms: 0 + -3 = -3
8n = -3

Divide each side by '8'.
n = -0.375

Simplifying
n = -0.375
Solution
n = {-0.5, -0.375}