(6+v)(4v-7)=0

Solution for (6+v)(4v-7)=0 equation:

Simplifying
(6 + v)(4v + -7) = 0

Reorder the terms:
(6 + v)(-7 + 4v) = 0

Multiply (6 + v) * (-7 + 4v)
(6(-7 + 4v) + v(-7 + 4v)) = 0
((-7 * 6 + 4v * 6) + v(-7 + 4v)) = 0
((-42 + 24v) + v(-7 + 4v)) = 0
(-42 + 24v + (-7 * v + 4v * v)) = 0
(-42 + 24v + (-7v + 4v2)) = 0

Combine like terms: 24v + -7v = 17v
(-42 + 17v + 4v2) = 0

Solving
-42 + 17v + 4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-6 + -1v)(7 + -4v) = 0

Subproblem 1
Set the factor '(-6 + -1v)' equal to zero and attempt to solve:

Simplifying
-6 + -1v = 0

Solving
-6 + -1v = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1v = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1v = 0 + 6
-1v = 0 + 6

Combine like terms: 0 + 6 = 6
-1v = 6

Divide each side by '-1'.
v = -6

Simplifying
v = -6
Subproblem 2
Set the factor '(7 + -4v)' equal to zero and attempt to solve:

Simplifying
7 + -4v = 0

Solving
7 + -4v = 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 + -4v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4v = 0 + -7
-4v = 0 + -7

Combine like terms: 0 + -7 = -7
-4v = -7

Divide each side by '-4'.
v = 1.75

Simplifying
v = 1.75
Solution
v = {-6, 1.75}