1n(n^2+12)=1n(-9n-2)

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Solution for 1n(n^2+12)=1n(-9n-2) equation: 


Simplifying
1n(n2 + 12) = 1n(-9n + -2)

Reorder the terms:
1n(12 + n2) = 1n(-9n + -2)
(12 * 1n + n2 * 1n) = 1n(-9n + -2)
(12n + 1n3) = 1n(-9n + -2)

Reorder the terms:
12n + 1n3 = 1n(-2 + -9n)
12n + 1n3 = (-2 * 1n + -9n * 1n)
12n + 1n3 = (-2n + -9n2)

Solving
12n + 1n3 = -2n + -9n2

Solving for variable 'n'.

Reorder the terms:
12n + 2n + 9n2 + 1n3 = -2n + -9n2 + 2n + 9n2

Combine like terms: 12n + 2n = 14n
14n + 9n2 + 1n3 = -2n + -9n2 + 2n + 9n2

Reorder the terms:
14n + 9n2 + 1n3 = -2n + 2n + -9n2 + 9n2

Combine like terms: -2n + 2n = 0
14n + 9n2 + 1n3 = 0 + -9n2 + 9n2
14n + 9n2 + 1n3 = -9n2 + 9n2

Combine like terms: -9n2 + 9n2 = 0
14n + 9n2 + 1n3 = 0

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

Factor a trinomial.
n((7 + n)(2 + n)) = 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 '(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 '(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 = {0, -7, -2}

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