7v^2+55v+42=0

Solution for 7v^2+55v+42=0 equation:

Simplifying
7v2 + 55v + 42 = 0

Reorder the terms:
42 + 55v + 7v2 = 0

Solving
42 + 55v + 7v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(7 + v)(6 + 7v) = 0

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

Simplifying
7 + v = 0

Solving
7 + v = 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 + v = 0 + -7

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

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

Simplifying
v = -7
Subproblem 2
Set the factor '(6 + 7v)' equal to zero and attempt to solve:

Simplifying
6 + 7v = 0

Solving
6 + 7v = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7v = 0 + -6
7v = 0 + -6

Combine like terms: 0 + -6 = -6
7v = -6

Divide each side by '7'.
v = -0.8571428571

Simplifying
v = -0.8571428571
Solution
v = {-7, -0.8571428571}