(2n+2)(4n+5)=

Solution for (2n+2)(4n+5)= equation:

Simplifying
(2n + 2)(4n + 5) = 0

Reorder the terms:
(2 + 2n)(4n + 5) = 0

Reorder the terms:
(2 + 2n)(5 + 4n) = 0

Multiply (2 + 2n) * (5 + 4n)
(2(5 + 4n) + 2n * (5 + 4n)) = 0
((5 * 2 + 4n * 2) + 2n * (5 + 4n)) = 0
((10 + 8n) + 2n * (5 + 4n)) = 0
(10 + 8n + (5 * 2n + 4n * 2n)) = 0
(10 + 8n + (10n + 8n2)) = 0

Combine like terms: 8n + 10n = 18n
(10 + 18n + 8n2) = 0

Solving
10 + 18n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 9n + 4n2) = 0

Factor a trinomial.
2((5 + 4n)(1 + n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + 4n)' equal to zero and attempt to solve:

Simplifying
5 + 4n = 0

Solving
5 + 4n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + 4n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4n = 0 + -5
4n = 0 + -5

Combine like terms: 0 + -5 = -5
4n = -5

Divide each side by '4'.
n = -1.25

Simplifying
n = -1.25
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

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

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

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

Simplifying
n = -1
Solution
n = {-1.25, -1}