(4n+3)(4n+1)=

Solution for (4n+3)(4n+1)= equation:

Simplifying
(4n + 3)(4n + 1) = 0

Reorder the terms:
(3 + 4n)(4n + 1) = 0

Reorder the terms:
(3 + 4n)(1 + 4n) = 0

Multiply (3 + 4n) * (1 + 4n)
(3(1 + 4n) + 4n * (1 + 4n)) = 0
((1 * 3 + 4n * 3) + 4n * (1 + 4n)) = 0
((3 + 12n) + 4n * (1 + 4n)) = 0
(3 + 12n + (1 * 4n + 4n * 4n)) = 0
(3 + 12n + (4n + 16n2)) = 0

Combine like terms: 12n + 4n = 16n
(3 + 16n + 16n2) = 0

Solving
3 + 16n + 16n2 = 0

Solving for variable 'n'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 4n)' equal to zero and attempt to solve:

Simplifying
1 + 4n = 0

Solving
1 + 4n = 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 + 4n = 0 + -1

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

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

Divide each side by '4'.
n = -0.25

Simplifying
n = -0.25
Solution
n = {-0.75, -0.25}