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

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Solution for 7(n+4)(n+7)=0 equation: 


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

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

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

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

Combine like terms: 4n + 7n = 11n
7(28 + 11n + n2) = 0
(28 * 7 + 11n * 7 + n2 * 7) = 0
(196 + 77n + 7n2) = 0

Solving
196 + 77n + 7n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '7'.
7(28 + 11n + n2) = 0

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

Ignore the factor 7.

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 '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

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

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

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

Simplifying
n = -4
Solution
n = {-7, -4}

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