(3v+4)(v+6)=0

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Solution for (3v+4)(v+6)=0 equation:


Simplifying
(3v + 4)(v + 6) = 0

Reorder the terms:
(4 + 3v)(v + 6) = 0

Reorder the terms:
(4 + 3v)(6 + v) = 0

Multiply (4 + 3v) * (6 + v)
(4(6 + v) + 3v * (6 + v)) = 0
((6 * 4 + v * 4) + 3v * (6 + v)) = 0
((24 + 4v) + 3v * (6 + v)) = 0
(24 + 4v + (6 * 3v + v * 3v)) = 0
(24 + 4v + (18v + 3v2)) = 0

Combine like terms: 4v + 18v = 22v
(24 + 22v + 3v2) = 0

Solving
24 + 22v + 3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(6 + v)(4 + 3v) = 0

Subproblem 1

Set the factor '(6 + v)' equal to zero and attempt to solve: Simplifying 6 + v = 0 Solving 6 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + v = 0 + -6 v = 0 + -6 Combine like terms: 0 + -6 = -6 v = -6 Simplifying v = -6

Subproblem 2

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

Solution

v = {-6, -1.333333333}

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