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

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


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

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

Multiply (-7 + 3v) * (7 + v)
(-7(7 + v) + 3v * (7 + v)) = 0
((7 * -7 + v * -7) + 3v * (7 + v)) = 0
((-49 + -7v) + 3v * (7 + v)) = 0
(-49 + -7v + (7 * 3v + v * 3v)) = 0
(-49 + -7v + (21v + 3v2)) = 0

Combine like terms: -7v + 21v = 14v
(-49 + 14v + 3v2) = 0

Solving
-49 + 14v + 3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-7 + -1v)(7 + -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 '(7 + -3v)' equal to zero and attempt to solve:

Simplifying
7 + -3v = 0

Solving
7 + -3v = 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 + -3v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3v = 0 + -7
-3v = 0 + -7

Combine like terms: 0 + -7 = -7
-3v = -7

Divide each side by '-3'.
v = 2.333333333

Simplifying
v = 2.333333333
Solution
v = {-7, 2.333333333}

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