=N^2+8N+7

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Solution for =N^2+8N+7 equation: 


Simplifying
0 = N2 + 8N + 7

Reorder the terms:
0 = 7 + 8N + N2

Solving
0 = 7 + 8N + N2

Solving for variable 'N'.

Combine like terms: 0 + -7 = -7
-7 + -8N + -1N2 = 7 + 8N + N2 + -7 + -8N + -1N2

Reorder the terms:
-7 + -8N + -1N2 = 7 + -7 + 8N + -8N + N2 + -1N2

Combine like terms: 7 + -7 = 0
-7 + -8N + -1N2 = 0 + 8N + -8N + N2 + -1N2
-7 + -8N + -1N2 = 8N + -8N + N2 + -1N2

Combine like terms: 8N + -8N = 0
-7 + -8N + -1N2 = 0 + N2 + -1N2
-7 + -8N + -1N2 = N2 + -1N2

Combine like terms: N2 + -1N2 = 0
-7 + -8N + -1N2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 8N + N2) = 0

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

Ignore the factor -1.

Subproblem 1
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 2
Set the factor '(1 + N)' equal to zero and attempt to solve:

Simplifying
1 + N = 0

Solving
1 + N = 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 + N = 0 + -1

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

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

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

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