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

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


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

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

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

Multiply (-3 + 2v) * (7 + 3v)
(-3(7 + 3v) + 2v * (7 + 3v)) = 0
((7 * -3 + 3v * -3) + 2v * (7 + 3v)) = 0
((-21 + -9v) + 2v * (7 + 3v)) = 0
(-21 + -9v + (7 * 2v + 3v * 2v)) = 0
(-21 + -9v + (14v + 6v2)) = 0

Combine like terms: -9v + 14v = 5v
(-21 + 5v + 6v2) = 0

Solving
-21 + 5v + 6v2 = 0

Solving for variable 'v'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -2v)' equal to zero and attempt to solve:

Simplifying
3 + -2v = 0

Solving
3 + -2v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -2v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2v = 0 + -3
-2v = 0 + -3

Combine like terms: 0 + -3 = -3
-2v = -3

Divide each side by '-2'.
v = 1.5

Simplifying
v = 1.5
Solution
v = {-2.333333333, 1.5}

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