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

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

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

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

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

Combine like terms: 7v + 6v = 13v
(-21 + 13v + -2v2) = 0

Solving
-21 + 13v + -2v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-7 + 2v)(3 + -1v) = 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 '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 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 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Solution
v = {3.5, 3}