v^2=18-3v

Solution for v^2=18-3v equation:

Simplifying
v2 = 18 + -3v

Solving
v2 = 18 + -3v

Solving for variable 'v'.

Reorder the terms:
-18 + 3v + v2 = 18 + -3v + -18 + 3v

Reorder the terms:
-18 + 3v + v2 = 18 + -18 + -3v + 3v

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

Combine like terms: -3v + 3v = 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}