(v-5)(v+8)=-22

Solution for (v-5)(v+8)=-22 equation:

Simplifying
(v + -5)(v + 8) = -22

Reorder the terms:
(-5 + v)(v + 8) = -22

Reorder the terms:
(-5 + v)(8 + v) = -22

Multiply (-5 + v) * (8 + v)
(-5(8 + v) + v(8 + v)) = -22
((8 * -5 + v * -5) + v(8 + v)) = -22
((-40 + -5v) + v(8 + v)) = -22
(-40 + -5v + (8 * v + v * v)) = -22
(-40 + -5v + (8v + v2)) = -22

Combine like terms: -5v + 8v = 3v
(-40 + 3v + v2) = -22

Solving
-40 + 3v + v2 = -22

Solving for variable 'v'.

Reorder the terms:
-40 + 22 + 3v + v2 = -22 + 22

Combine like terms: -40 + 22 = -18
-18 + 3v + v2 = -22 + 22

Combine like terms: -22 + 22 = 0
-18 + 3v + v2 = 0

Factor a trinomial.
(-6 + -1v)(3 + -1v) = 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 '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 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 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Solution
v = {-6, 3}