(1+v)(4v+3)=0

Solution for (1+v)(4v+3)=0 equation:

Simplifying
(1 + v)(4v + 3) = 0

Reorder the terms:
(1 + v)(3 + 4v) = 0

Multiply (1 + v) * (3 + 4v)
(1(3 + 4v) + v(3 + 4v)) = 0
((3 * 1 + 4v * 1) + v(3 + 4v)) = 0
((3 + 4v) + v(3 + 4v)) = 0
(3 + 4v + (3 * v + 4v * v)) = 0
(3 + 4v + (3v + 4v2)) = 0

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

Solving
3 + 7v + 4v2 = 0

Solving for variable 'v'.

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

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

Simplifying
1 + v = 0

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

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

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

Simplifying
v = -1
Subproblem 2
Set the factor '(3 + 4v)' equal to zero and attempt to solve:

Simplifying
3 + 4v = 0

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

Combine like terms: 3 + -3 = 0
0 + 4v = 0 + -3
4v = 0 + -3

Combine like terms: 0 + -3 = -3
4v = -3

Divide each side by '4'.
v = -0.75

Simplifying
v = -0.75
Solution
v = {-1, -0.75}