(6n^2-6n-5)=(7n^2+6n-5)

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Solution for (6n^2-6n-5)=(7n^2+6n-5) equation: 


Simplifying
(6n2 + -6n + -5) = (7n2 + 6n + -5)

Reorder the terms:
(-5 + -6n + 6n2) = (7n2 + 6n + -5)

Remove parenthesis around (-5 + -6n + 6n2)
-5 + -6n + 6n2 = (7n2 + 6n + -5)

Reorder the terms:
-5 + -6n + 6n2 = (-5 + 6n + 7n2)

Remove parenthesis around (-5 + 6n + 7n2)
-5 + -6n + 6n2 = -5 + 6n + 7n2

Add '5' to each side of the equation.
-5 + -6n + 5 + 6n2 = -5 + 6n + 5 + 7n2

Reorder the terms:
-5 + 5 + -6n + 6n2 = -5 + 6n + 5 + 7n2

Combine like terms: -5 + 5 = 0
0 + -6n + 6n2 = -5 + 6n + 5 + 7n2
-6n + 6n2 = -5 + 6n + 5 + 7n2

Reorder the terms:
-6n + 6n2 = -5 + 5 + 6n + 7n2

Combine like terms: -5 + 5 = 0
-6n + 6n2 = 0 + 6n + 7n2
-6n + 6n2 = 6n + 7n2

Solving
-6n + 6n2 = 6n + 7n2

Solving for variable 'n'.

Reorder the terms:
-6n + -6n + 6n2 + -7n2 = 6n + 7n2 + -6n + -7n2

Combine like terms: -6n + -6n = -12n
-12n + 6n2 + -7n2 = 6n + 7n2 + -6n + -7n2

Combine like terms: 6n2 + -7n2 = -1n2
-12n + -1n2 = 6n + 7n2 + -6n + -7n2

Reorder the terms:
-12n + -1n2 = 6n + -6n + 7n2 + -7n2

Combine like terms: 6n + -6n = 0
-12n + -1n2 = 0 + 7n2 + -7n2
-12n + -1n2 = 7n2 + -7n2

Combine like terms: 7n2 + -7n2 = 0
-12n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), '-1n'.
-1n(12 + n) = 0

Ignore the factor -1.

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

Simplifying
12 + n = 0

Solving
12 + n = 0

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

Add '-12' to each side of the equation.
12 + -12 + n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + n = 0 + -12
n = 0 + -12

Combine like terms: 0 + -12 = -12
n = -12

Simplifying
n = -12
Solution
n = {0, -12}

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