(2v+7)(3v-1)=0

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Solution for (2v+7)(3v-1)=0 equation:


Simplifying
(2v + 7)(3v + -1) = 0

Reorder the terms:
(7 + 2v)(3v + -1) = 0

Reorder the terms:
(7 + 2v)(-1 + 3v) = 0

Multiply (7 + 2v) * (-1 + 3v)
(7(-1 + 3v) + 2v * (-1 + 3v)) = 0
((-1 * 7 + 3v * 7) + 2v * (-1 + 3v)) = 0
((-7 + 21v) + 2v * (-1 + 3v)) = 0
(-7 + 21v + (-1 * 2v + 3v * 2v)) = 0
(-7 + 21v + (-2v + 6v2)) = 0

Combine like terms: 21v + -2v = 19v
(-7 + 19v + 6v2) = 0

Solving
-7 + 19v + 6v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-7 + -2v)(1 + -3v) = 0

Subproblem 1

Set the factor '(-7 + -2v)' equal to zero and attempt to solve: Simplifying -7 + -2v = 0 Solving -7 + -2v = 0 Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2v = 0 + 7 -2v = 0 + 7 Combine like terms: 0 + 7 = 7 -2v = 7 Divide each side by '-2'. v = -3.5 Simplifying v = -3.5

Subproblem 2

Set the factor '(1 + -3v)' equal to zero and attempt to solve: Simplifying 1 + -3v = 0 Solving 1 + -3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3v = 0 + -1 -3v = 0 + -1 Combine like terms: 0 + -1 = -1 -3v = -1 Divide each side by '-3'. v = 0.3333333333 Simplifying v = 0.3333333333

Solution

v = {-3.5, 0.3333333333}

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