(v^2+20v-59)=10

Solution for (v^2+20v-59)=10 equation:

Simplifying
(v2 + 20v + -59) = 10

Reorder the terms:
(-59 + 20v + v2) = 10

Remove parenthesis around (-59 + 20v + v2)
-59 + 20v + v2 = 10

Solving
-59 + 20v + v2 = 10

Solving for variable 'v'.

Reorder the terms:
-59 + -10 + 20v + v2 = 10 + -10

Combine like terms: -59 + -10 = -69
-69 + 20v + v2 = 10 + -10

Combine like terms: 10 + -10 = 0
-69 + 20v + v2 = 0

Factor a trinomial.
(-23 + -1v)(3 + -1v) = 0

Subproblem 1
Set the factor '(-23 + -1v)' equal to zero and attempt to solve:

Simplifying
-23 + -1v = 0

Solving
-23 + -1v = 0

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

Add '23' to each side of the equation.
-23 + 23 + -1v = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -1v = 0 + 23
-1v = 0 + 23

Combine like terms: 0 + 23 = 23
-1v = 23

Divide each side by '-1'.
v = -23

Simplifying
v = -23
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 = {-23, 3}