(7v+4)(3v-9)=0

Solution for (7v+4)(3v-9)=0 equation:

Simplifying
(7v + 4)(3v + -9) = 0

Reorder the terms:
(4 + 7v)(3v + -9) = 0

Reorder the terms:
(4 + 7v)(-9 + 3v) = 0

Multiply (4 + 7v) * (-9 + 3v)
(4(-9 + 3v) + 7v * (-9 + 3v)) = 0
((-9 * 4 + 3v * 4) + 7v * (-9 + 3v)) = 0
((-36 + 12v) + 7v * (-9 + 3v)) = 0
(-36 + 12v + (-9 * 7v + 3v * 7v)) = 0
(-36 + 12v + (-63v + 21v2)) = 0

Combine like terms: 12v + -63v = -51v
(-36 + -51v + 21v2) = 0

Solving
-36 + -51v + 21v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -17v + 7v2) = 0

Factor a trinomial.
3((-4 + -7v)(3 + -1v)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -7v)' equal to zero and attempt to solve:

Simplifying
-4 + -7v = 0

Solving
-4 + -7v = 0

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

Add '4' to each side of the equation.
-4 + 4 + -7v = 0 + 4

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

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

Divide each side by '-7'.
v = -0.5714285714

Simplifying
v = -0.5714285714
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 = {-0.5714285714, 3}