n^2(n-7)(n+7)=0

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Solution for n^2(n-7)(n+7)=0 equation: 


Simplifying
n2(n + -7)(n + 7) = 0

Reorder the terms:
n2(-7 + n)(n + 7) = 0

Reorder the terms:
n2(-7 + n)(7 + n) = 0

Multiply (-7 + n) * (7 + n)
n2(-7(7 + n) + n(7 + n)) = 0
n2((7 * -7 + n * -7) + n(7 + n)) = 0
n2((-49 + -7n) + n(7 + n)) = 0
n2(-49 + -7n + (7 * n + n * n)) = 0
n2(-49 + -7n + (7n + n2)) = 0

Combine like terms: -7n + 7n = 0
n2(-49 + 0 + n2) = 0
n2(-49 + n2) = 0
(-49 * n2 + n2 * n2) = 0
(-49n2 + n4) = 0

Solving
-49n2 + n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n2'.
n2(-49 + n2) = 0

Factor a difference between two squares.
n2((7 + n)(-7 + n)) = 0


Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

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

Simplifying
n2 = 0

Take the square root of each side:
n = {0}

Subproblem 2
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 3
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
Solution
n = {0, -7, 7}

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