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

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

Simplifying
(4v + -6)(7 + -1v) = 0

Reorder the terms:
(-6 + 4v)(7 + -1v) = 0

Multiply (-6 + 4v) * (7 + -1v)
(-6(7 + -1v) + 4v * (7 + -1v)) = 0
((7 * -6 + -1v * -6) + 4v * (7 + -1v)) = 0
((-42 + 6v) + 4v * (7 + -1v)) = 0
(-42 + 6v + (7 * 4v + -1v * 4v)) = 0
(-42 + 6v + (28v + -4v2)) = 0

Combine like terms: 6v + 28v = 34v
(-42 + 34v + -4v2) = 0

Solving
-42 + 34v + -4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 17v + -2v2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + v)' equal to zero and attempt to solve:

Simplifying
-7 + v = 0

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

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

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

Simplifying
v = 7
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 = {7, 1.5}