v^2=6v-9

Solution for v^2=6v-9 equation:

Simplifying
v2 = 6v + -9

Reorder the terms:
v2 = -9 + 6v

Solving
v2 = -9 + 6v

Solving for variable 'v'.

Reorder the terms:
9 + -6v + v2 = -9 + 6v + 9 + -6v

Reorder the terms:
9 + -6v + v2 = -9 + 9 + 6v + -6v

Combine like terms: -9 + 9 = 0
9 + -6v + v2 = 0 + 6v + -6v
9 + -6v + v2 = 6v + -6v

Combine like terms: 6v + -6v = 0
9 + -6v + v2 = 0

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

Subproblem 1
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
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 = {3, 3}