4v^2=-7v-3

Solution for 4v^2=-7v-3 equation:

Simplifying
4v2 = -7v + -3

Reorder the terms:
4v2 = -3 + -7v

Solving
4v2 = -3 + -7v

Solving for variable 'v'.

Reorder the terms:
3 + 7v + 4v2 = -3 + -7v + 3 + 7v

Reorder the terms:
3 + 7v + 4v2 = -3 + 3 + -7v + 7v

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

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

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}