8v^2+41v-42=0

Solution for 8v^2+41v-42=0 equation:

Simplifying
8v2 + 41v + -42 = 0

Reorder the terms:
-42 + 41v + 8v2 = 0

Solving
-42 + 41v + 8v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-6 + -1v)(7 + -8v) = 0

Subproblem 1
Set the factor '(-6 + -1v)' equal to zero and attempt to solve:

Simplifying
-6 + -1v = 0

Solving
-6 + -1v = 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 + -1v = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1v = 0 + 6
-1v = 0 + 6

Combine like terms: 0 + 6 = 6
-1v = 6

Divide each side by '-1'.
v = -6

Simplifying
v = -6
Subproblem 2
Set the factor '(7 + -8v)' equal to zero and attempt to solve:

Simplifying
7 + -8v = 0

Solving
7 + -8v = 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 + -8v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8v = 0 + -7
-8v = 0 + -7

Combine like terms: 0 + -7 = -7
-8v = -7

Divide each side by '-8'.
v = 0.875

Simplifying
v = 0.875
Solution
v = {-6, 0.875}