(7v+1)(v-3)=0

Solution for (7v+1)(v-3)=0 equation:

Simplifying
(7v + 1)(v + -3) = 0

Reorder the terms:
(1 + 7v)(v + -3) = 0

Reorder the terms:
(1 + 7v)(-3 + v) = 0

Multiply (1 + 7v) * (-3 + v)
(1(-3 + v) + 7v * (-3 + v)) = 0
((-3 * 1 + v * 1) + 7v * (-3 + v)) = 0
((-3 + 1v) + 7v * (-3 + v)) = 0
(-3 + 1v + (-3 * 7v + v * 7v)) = 0
(-3 + 1v + (-21v + 7v2)) = 0

Combine like terms: 1v + -21v = -20v
(-3 + -20v + 7v2) = 0

Solving
-3 + -20v + 7v2 = 0

Solving for variable 'v'.

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

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

Simplifying
-1 + -7v = 0

Solving
-1 + -7v = 0

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

Add '1' to each side of the equation.
-1 + 1 + -7v = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7v = 0 + 1
-7v = 0 + 1

Combine like terms: 0 + 1 = 1
-7v = 1

Divide each side by '-7'.
v = -0.1428571429

Simplifying
v = -0.1428571429
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 = {-0.1428571429, 3}