2n^2-1=-n

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Solution for 2n^2-1=-n equation:


Simplifying
2n2 + -1 = -1n

Reorder the terms:
-1 + 2n2 = -1n

Solving
-1 + 2n2 = -1n

Solving for variable 'n'.

Reorder the terms:
-1 + n + 2n2 = -1n + n

Combine like terms: -1n + n = 0
-1 + n + 2n2 = 0

Factor a trinomial.
(-1 + -1n)(1 + -2n) = 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 '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 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 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5

Solution

n = {-1, 0.5}

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