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

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

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

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

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

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

Combine like terms: -16n + 2n = -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((-1 + -4n)(2 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
n = {-0.25, 2}