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

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


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

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

Multiply (7 + -1v) * (2 + 3v)
(7(2 + 3v) + -1v * (2 + 3v)) = 0
((2 * 7 + 3v * 7) + -1v * (2 + 3v)) = 0
((14 + 21v) + -1v * (2 + 3v)) = 0
(14 + 21v + (2 * -1v + 3v * -1v)) = 0
(14 + 21v + (-2v + -3v2)) = 0

Combine like terms: 21v + -2v = 19v
(14 + 19v + -3v2) = 0

Solving
14 + 19v + -3v2 = 0

Solving for variable 'v'.

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

Subproblem 1

Set the factor '(7 + -1v)' equal to zero and attempt to solve: Simplifying 7 + -1v = 0 Solving 7 + -1v = 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 + -1v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1v = 0 + -7 -1v = 0 + -7 Combine like terms: 0 + -7 = -7 -1v = -7 Divide each side by '-1'. v = 7 Simplifying v = 7

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 = {7, -0.6666666667}

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