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

Solution for (4v+7)(1-v)=0 equation:

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

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

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

Combine like terms: -7v + 4v = -3v
(7 + -3v + -4v2) = 0

Solving
7 + -3v + -4v2 = 0

Solving for variable 'v'.

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

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

Simplifying
1 + -1v = 0

Solving
1 + -1v = 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 + -1v = 0 + -1

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

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

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

Simplifying
v = 1
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 = {1, -1.75}