n^2+2n-15=8n-8

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Solution for n^2+2n-15=8n-8 equation: 


Simplifying
n2 + 2n + -15 = 8n + -8

Reorder the terms:
-15 + 2n + n2 = 8n + -8

Reorder the terms:
-15 + 2n + n2 = -8 + 8n

Solving
-15 + 2n + n2 = -8 + 8n

Solving for variable 'n'.

Reorder the terms:
-15 + 8 + 2n + -8n + n2 = -8 + 8n + 8 + -8n

Combine like terms: -15 + 8 = -7
-7 + 2n + -8n + n2 = -8 + 8n + 8 + -8n

Combine like terms: 2n + -8n = -6n
-7 + -6n + n2 = -8 + 8n + 8 + -8n

Reorder the terms:
-7 + -6n + n2 = -8 + 8 + 8n + -8n

Combine like terms: -8 + 8 = 0
-7 + -6n + n2 = 0 + 8n + -8n
-7 + -6n + n2 = 8n + -8n

Combine like terms: 8n + -8n = 0
-7 + -6n + n2 = 0

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


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

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1n = 0 + 1

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

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

Divide each side by '-1'.
n = -1

Simplifying
n = -1

Subproblem 2
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

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {-1, 7}

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