(n+2)(4n+6)=

Solution for (n+2)(4n+6)= equation:

Simplifying
(n + 2)(4n + 6) = 0

Reorder the terms:
(2 + n)(4n + 6) = 0

Reorder the terms:
(2 + n)(6 + 4n) = 0

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

Combine like terms: 8n + 6n = 14n
(12 + 14n + 4n2) = 0

Solving
12 + 14n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 7n + 2n2) = 0

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

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

Simplifying
2 + n = 0

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

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

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

Simplifying
n = -2
Subproblem 2
Set the factor '(3 + 2n)' equal to zero and attempt to solve:

Simplifying
3 + 2n = 0

Solving
3 + 2n = 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 + 2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2n = 0 + -3
2n = 0 + -3

Combine like terms: 0 + -3 = -3
2n = -3

Divide each side by '2'.
n = -1.5

Simplifying
n = -1.5
Solution
n = {-2, -1.5}