(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 = 1v
(-3 + 1v + 4v2) = 0

Solving
-3 + 1v + 4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-1 + -1v)(3 + -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 '(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}