5v^2-24v-31=5

Solution for 5v^2-24v-31=5 equation:

Simplifying
5v2 + -24v + -31 = 5

Reorder the terms:
-31 + -24v + 5v2 = 5

Solving
-31 + -24v + 5v2 = 5

Solving for variable 'v'.

Reorder the terms:
-31 + -5 + -24v + 5v2 = 5 + -5

Combine like terms: -31 + -5 = -36
-36 + -24v + 5v2 = 5 + -5

Combine like terms: 5 + -5 = 0
-36 + -24v + 5v2 = 0

Factor a trinomial.
(-6 + -5v)(6 + -1v) = 0

Subproblem 1
Set the factor '(-6 + -5v)' equal to zero and attempt to solve:

Simplifying
-6 + -5v = 0

Solving
-6 + -5v = 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 + -5v = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5v = 0 + 6
-5v = 0 + 6

Combine like terms: 0 + 6 = 6
-5v = 6

Divide each side by '-5'.
v = -1.2

Simplifying
v = -1.2
Subproblem 2
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
Solution
v = {-1.2, 6}