n^2+7=-8n

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Solution for n^2+7=-8n equation:


Simplifying
n2 + 7 = -8n

Reorder the terms:
7 + n2 = -8n

Solving
7 + n2 = -8n

Solving for variable 'n'.

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

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

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

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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