n^2-8=-7n

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


Simplifying
n2 + -8 = -7n

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

Solving
-8 + n2 = -7n

Solving for variable 'n'.

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

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

Factor a trinomial.
(-8 + -1n)(1 + -1n) = 0

Subproblem 1

Set the factor '(-8 + -1n)' equal to zero and attempt to solve: Simplifying -8 + -1n = 0 Solving -8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1n = 0 + 8 -1n = 0 + 8 Combine like terms: 0 + 8 = 8 -1n = 8 Divide each side by '-1'. n = -8 Simplifying n = -8

Subproblem 2

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

Solution

n = {-8, 1}

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