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

Solution for (n+2)(4n-1)=0 equation:

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

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

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

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

Combine like terms: 8n + -1n = 7n
(-2 + 7n + 4n2) = 0

Solving
-2 + 7n + 4n2 = 0

Solving for variable 'n'.

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

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}