v^2+9v=10

Solution for v^2+9v=10 equation:

Simplifying
v2 + 9v = 10

Reorder the terms:
9v + v2 = 10

Solving
9v + v2 = 10

Solving for variable 'v'.

Reorder the terms:
-10 + 9v + v2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 9v + v2 = 0

Factor a trinomial.
(-10 + -1v)(1 + -1v) = 0

Subproblem 1
Set the factor '(-10 + -1v)' equal to zero and attempt to solve:

Simplifying
-10 + -1v = 0

Solving
-10 + -1v = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1v = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1v = 0 + 10
-1v = 0 + 10

Combine like terms: 0 + 10 = 10
-1v = 10

Divide each side by '-1'.
v = -10

Simplifying
v = -10
Subproblem 2
Set the factor '(1 + -1v)' equal to zero and attempt to solve:

Simplifying
1 + -1v = 0

Solving
1 + -1v = 0

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

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

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

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

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

Simplifying
v = 1
Solution
v = {-10, 1}