2v^2=18+9v

Solution for 2v^2=18+9v equation:

Simplifying
2v2 = 18 + 9v

Solving
2v2 = 18 + 9v

Solving for variable 'v'.

Reorder the terms:
-18 + -9v + 2v2 = 18 + 9v + -18 + -9v

Reorder the terms:
-18 + -9v + 2v2 = 18 + -18 + 9v + -9v

Combine like terms: 18 + -18 = 0
-18 + -9v + 2v2 = 0 + 9v + -9v
-18 + -9v + 2v2 = 9v + -9v

Combine like terms: 9v + -9v = 0
-18 + -9v + 2v2 = 0

Factor a trinomial.
(-3 + -2v)(6 + -1v) = 0

Subproblem 1
Set the factor '(-3 + -2v)' equal to zero and attempt to solve:

Simplifying
-3 + -2v = 0

Solving
-3 + -2v = 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 + -2v = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2v = 0 + 3
-2v = 0 + 3

Combine like terms: 0 + 3 = 3
-2v = 3

Divide each side by '-2'.
v = -1.5

Simplifying
v = -1.5
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 = {-1.5, 6}