(3n+2)(n-9)=0

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Solution for (3n+2)(n-9)=0 equation:


Simplifying
(3n + 2)(n + -9) = 0

Reorder the terms:
(2 + 3n)(n + -9) = 0

Reorder the terms:
(2 + 3n)(-9 + n) = 0

Multiply (2 + 3n) * (-9 + n)
(2(-9 + n) + 3n * (-9 + n)) = 0
((-9 * 2 + n * 2) + 3n * (-9 + n)) = 0
((-18 + 2n) + 3n * (-9 + n)) = 0
(-18 + 2n + (-9 * 3n + n * 3n)) = 0
(-18 + 2n + (-27n + 3n2)) = 0

Combine like terms: 2n + -27n = -25n
(-18 + -25n + 3n2) = 0

Solving
-18 + -25n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-2 + -3n)(9 + -1n) = 0

Subproblem 1

Set the factor '(-2 + -3n)' equal to zero and attempt to solve: Simplifying -2 + -3n = 0 Solving -2 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3n = 0 + 2 -3n = 0 + 2 Combine like terms: 0 + 2 = 2 -3n = 2 Divide each side by '-3'. n = -0.6666666667 Simplifying n = -0.6666666667

Subproblem 2

Set the factor '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 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 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9

Solution

n = {-0.6666666667, 9}

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