(2n+1)(n+1)=0

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Solution for (2n+1)(n+1)=0 equation:


Simplifying
(2n + 1)(n + 1) = 0

Reorder the terms:
(1 + 2n)(n + 1) = 0

Reorder the terms:
(1 + 2n)(1 + n) = 0

Multiply (1 + 2n) * (1 + n)
(1(1 + n) + 2n * (1 + n)) = 0
((1 * 1 + n * 1) + 2n * (1 + n)) = 0
((1 + 1n) + 2n * (1 + n)) = 0
(1 + 1n + (1 * 2n + n * 2n)) = 0
(1 + 1n + (2n + 2n2)) = 0

Combine like terms: 1n + 2n = 3n
(1 + 3n + 2n2) = 0

Solving
1 + 3n + 2n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + n)(1 + 2n) = 0

Subproblem 1

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

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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