v^2=54-3v

Solution for v^2=54-3v equation:

Simplifying
v2 = 54 + -3v

Solving
v2 = 54 + -3v

Solving for variable 'v'.

Reorder the terms:
-54 + 3v + v2 = 54 + -3v + -54 + 3v

Reorder the terms:
-54 + 3v + v2 = 54 + -54 + -3v + 3v

Combine like terms: 54 + -54 = 0
-54 + 3v + v2 = 0 + -3v + 3v
-54 + 3v + v2 = -3v + 3v

Combine like terms: -3v + 3v = 0
-54 + 3v + v2 = 0

Factor a trinomial.
(-9 + -1v)(6 + -1v) = 0

Subproblem 1
Set the factor '(-9 + -1v)' equal to zero and attempt to solve:

Simplifying
-9 + -1v = 0

Solving
-9 + -1v = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1v = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1v = 0 + 9
-1v = 0 + 9

Combine like terms: 0 + 9 = 9
-1v = 9

Divide each side by '-1'.
v = -9

Simplifying
v = -9
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 = {-9, 6}