(7v+3)(4v-12)=0

Solution for (7v+3)(4v-12)=0 equation:

Simplifying
(7v + 3)(4v + -12) = 0

Reorder the terms:
(3 + 7v)(4v + -12) = 0

Reorder the terms:
(3 + 7v)(-12 + 4v) = 0

Multiply (3 + 7v) * (-12 + 4v)
(3(-12 + 4v) + 7v * (-12 + 4v)) = 0
((-12 * 3 + 4v * 3) + 7v * (-12 + 4v)) = 0
((-36 + 12v) + 7v * (-12 + 4v)) = 0
(-36 + 12v + (-12 * 7v + 4v * 7v)) = 0
(-36 + 12v + (-84v + 28v2)) = 0

Combine like terms: 12v + -84v = -72v
(-36 + -72v + 28v2) = 0

Solving
-36 + -72v + 28v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -18v + 7v2) = 0

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

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

Simplifying
-3 + -7v = 0

Solving
-3 + -7v = 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 + -7v = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7v = 0 + 3
-7v = 0 + 3

Combine like terms: 0 + 3 = 3
-7v = 3

Divide each side by '-7'.
v = -0.4285714286

Simplifying
v = -0.4285714286
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 = {-0.4285714286, 3}