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

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

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

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

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

Combine like terms: 6v + -7v = -1v
(-21 + -1v + 2v2) = 0

Solving
-21 + -1v + 2v2 = 0

Solving for variable 'v'.

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

Subproblem 1
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
Subproblem 2
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
Solution
v = {-3, 3.5}