(n+7)(4n+8)=

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Solution for (n+7)(4n+8)= equation: 


Simplifying
(n + 7)(4n + 8) = 0

Reorder the terms:
(7 + n)(4n + 8) = 0

Reorder the terms:
(7 + n)(8 + 4n) = 0

Multiply (7 + n) * (8 + 4n)
(7(8 + 4n) + n(8 + 4n)) = 0
((8 * 7 + 4n * 7) + n(8 + 4n)) = 0
((56 + 28n) + n(8 + 4n)) = 0
(56 + 28n + (8 * n + 4n * n)) = 0
(56 + 28n + (8n + 4n2)) = 0

Combine like terms: 28n + 8n = 36n
(56 + 36n + 4n2) = 0

Solving
56 + 36n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(14 + 9n + n2) = 0

Factor a trinomial.
4((7 + n)(2 + n)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve:

Simplifying
7 + n = 0

Solving
7 + n = 0

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

Add '-7' to each side of the equation.
7 + -7 + n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + n = 0 + -7
n = 0 + -7

Combine like terms: 0 + -7 = -7
n = -7

Simplifying
n = -7

Subproblem 2
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
Solution
n = {-7, -2}

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