(4n+3)(n+9)=0

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Solution for (4n+3)(n+9)=0 equation:


Simplifying
(4n + 3)(n + 9) = 0

Reorder the terms:
(3 + 4n)(n + 9) = 0

Reorder the terms:
(3 + 4n)(9 + n) = 0

Multiply (3 + 4n) * (9 + n)
(3(9 + n) + 4n * (9 + n)) = 0
((9 * 3 + n * 3) + 4n * (9 + n)) = 0
((27 + 3n) + 4n * (9 + n)) = 0
(27 + 3n + (9 * 4n + n * 4n)) = 0
(27 + 3n + (36n + 4n2)) = 0

Combine like terms: 3n + 36n = 39n
(27 + 39n + 4n2) = 0

Solving
27 + 39n + 4n2 = 0

Solving for variable 'n'.

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

Subproblem 1

Set the factor '(9 + n)' equal to zero and attempt to solve: Simplifying 9 + n = 0 Solving 9 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + n = 0 + -9 n = 0 + -9 Combine like terms: 0 + -9 = -9 n = -9 Simplifying n = -9

Subproblem 2

Set the factor '(3 + 4n)' equal to zero and attempt to solve: Simplifying 3 + 4n = 0 Solving 3 + 4n = 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 + 4n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4n = 0 + -3 4n = 0 + -3 Combine like terms: 0 + -3 = -3 4n = -3 Divide each side by '4'. n = -0.75 Simplifying n = -0.75

Solution

n = {-9, -0.75}

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