(3n+4)(n+3)=0

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Solution for (3n+4)(n+3)=0 equation:


Simplifying
(3n + 4)(n + 3) = 0

Reorder the terms:
(4 + 3n)(n + 3) = 0

Reorder the terms:
(4 + 3n)(3 + n) = 0

Multiply (4 + 3n) * (3 + n)
(4(3 + n) + 3n * (3 + n)) = 0
((3 * 4 + n * 4) + 3n * (3 + n)) = 0
((12 + 4n) + 3n * (3 + n)) = 0
(12 + 4n + (3 * 3n + n * 3n)) = 0
(12 + 4n + (9n + 3n2)) = 0

Combine like terms: 4n + 9n = 13n
(12 + 13n + 3n2) = 0

Solving
12 + 13n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + n)(4 + 3n) = 0

Subproblem 1

Set the factor '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3

Subproblem 2

Set the factor '(4 + 3n)' equal to zero and attempt to solve: Simplifying 4 + 3n = 0 Solving 4 + 3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3n = 0 + -4 3n = 0 + -4 Combine like terms: 0 + -4 = -4 3n = -4 Divide each side by '3'. n = -1.333333333 Simplifying n = -1.333333333

Solution

n = {-3, -1.333333333}

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