N(n-7)(n+3)=0

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Solution for N(n-7)(n+3)=0 equation: 


Simplifying
N(n + -7)(n + 3) = 0

Reorder the terms:
N(-7 + n)(n + 3) = 0

Reorder the terms:
N(-7 + n)(3 + n) = 0

Multiply (-7 + n) * (3 + n)
N(-7(3 + n) + n(3 + n)) = 0
N((3 * -7 + n * -7) + n(3 + n)) = 0
N((-21 + -7n) + n(3 + n)) = 0
N(-21 + -7n + (3 * n + n * n)) = 0
N(-21 + -7n + (3n + n2)) = 0

Combine like terms: -7n + 3n = -4n
N(-21 + -4n + n2) = 0
(-21 * N + -4n * N + n2 * N) = 0
(-21N + -4nN + n2N) = 0

Solving
-21N + -4nN + n2N = 0

Solving for variable 'N'.

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

Factor out the Greatest Common Factor (GCF), 'N'.
N(-21 + -4n + n2) = 0

Factor a trinomial.
N((-3 + -1n)(7 + -1n)) = 0


Subproblem 1
Set the factor 'N' equal to zero and attempt to solve:

Simplifying
N = 0

Solving
N = 0

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

Simplifying
N = 0

Subproblem 2
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 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 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Add 'n' to each side of the equation.
-1n + n = 3 + n

Combine like terms: -1n + n = 0
0 = 3 + n

Simplifying
0 = 3 + n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 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 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Add 'n' to each side of the equation.
-1n + n = -7 + n

Combine like terms: -1n + n = 0
0 = -7 + n

Simplifying
0 = -7 + n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
N = {0}

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