(3v+2)(9+v)=0

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


Simplifying
(3v + 2)(9 + v) = 0

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

Multiply (2 + 3v) * (9 + v)
(2(9 + v) + 3v * (9 + v)) = 0
((9 * 2 + v * 2) + 3v * (9 + v)) = 0
((18 + 2v) + 3v * (9 + v)) = 0
(18 + 2v + (9 * 3v + v * 3v)) = 0
(18 + 2v + (27v + 3v2)) = 0

Combine like terms: 2v + 27v = 29v
(18 + 29v + 3v2) = 0

Solving
18 + 29v + 3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(9 + v)(2 + 3v) = 0

Subproblem 1

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

Subproblem 2

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

Solution

v = {-9, -0.6666666667}

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