v^2+10v-75=0

Solution for v^2+10v-75=0 equation:

Simplifying
v2 + 10v + -75 = 0

Reorder the terms:
-75 + 10v + v2 = 0

Solving
-75 + 10v + v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-15 + -1v)(5 + -1v) = 0

Subproblem 1
Set the factor '(-15 + -1v)' equal to zero and attempt to solve:

Simplifying
-15 + -1v = 0

Solving
-15 + -1v = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1v = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1v = 0 + 15
-1v = 0 + 15

Combine like terms: 0 + 15 = 15
-1v = 15

Divide each side by '-1'.
v = -15

Simplifying
v = -15
Subproblem 2
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5
Solution
v = {-15, 5}