(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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