(4n-1)(2n+4)=

Solution for (4n-1)(2n+4)= equation:

Simplifying
(4n + -1)(2n + 4) = 0

Reorder the terms:
(-1 + 4n)(2n + 4) = 0

Reorder the terms:
(-1 + 4n)(4 + 2n) = 0

Multiply (-1 + 4n) * (4 + 2n)
(-1(4 + 2n) + 4n * (4 + 2n)) = 0
((4 * -1 + 2n * -1) + 4n * (4 + 2n)) = 0
((-4 + -2n) + 4n * (4 + 2n)) = 0
(-4 + -2n + (4 * 4n + 2n * 4n)) = 0
(-4 + -2n + (16n + 8n2)) = 0

Combine like terms: -2n + 16n = 14n
(-4 + 14n + 8n2) = 0

Solving
-4 + 14n + 8n2 = 0

Solving for variable 'n'.

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

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

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

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 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 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

Simplifying
n = -2
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 = {-2, 0.25}