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

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


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

Reorder the terms:
in(12 + n2) = in(-9n + -2)
(12 * in + n2 * in) = in(-9n + -2)
(12in + in3) = in(-9n + -2)

Reorder the terms:
12in + in3 = in(-2 + -9n)
12in + in3 = (-2 * in + -9n * in)
12in + in3 = (-2in + -9in2)

Solving
12in + in3 = -2in + -9in2

Solving for variable 'i'.

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

Add '2in' to each side of the equation.
12in + 2in + in3 = -2in + 2in + -9in2

Combine like terms: 12in + 2in = 14in
14in + in3 = -2in + 2in + -9in2

Combine like terms: -2in + 2in = 0
14in + in3 = 0 + -9in2
14in + in3 = -9in2

Add '9in2' to each side of the equation.
14in + 9in2 + in3 = -9in2 + 9in2

Combine like terms: -9in2 + 9in2 = 0
14in + 9in2 + in3 = 0

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

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


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

Simplifying
in = 0

Solving
in = 0

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

Simplifying
in = 0

The solution to this equation could not be determined.

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

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 i 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

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

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

Simplifying
0 = -7 + -1n

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

Simplifying
2 + n = 0

Solving
2 + n = 0

Move all terms containing i 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

Add '-1n' to each side of the equation.
n + -1n = -2 + -1n

Combine like terms: n + -1n = 0
0 = -2 + -1n

Simplifying
0 = -2 + -1n

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.

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