2(v+9)(-v+3)=0

Solution for 2(v+9)(-v+3)=0 equation:

Simplifying
2(v + 9)(-1v + 3) = 0

Reorder the terms:
2(9 + v)(-1v + 3) = 0

Reorder the terms:
2(9 + v)(3 + -1v) = 0

Multiply (9 + v) * (3 + -1v)
2(9(3 + -1v) + v(3 + -1v)) = 0
2((3 * 9 + -1v * 9) + v(3 + -1v)) = 0
2((27 + -9v) + v(3 + -1v)) = 0
2(27 + -9v + (3 * v + -1v * v)) = 0
2(27 + -9v + (3v + -1v2)) = 0

Combine like terms: -9v + 3v = -6v
2(27 + -6v + -1v2) = 0
(27 * 2 + -6v * 2 + -1v2 * 2) = 0
(54 + -12v + -2v2) = 0

Solving
54 + -12v + -2v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + -6v + -1v2) = 0

Factor a trinomial.
2((3 + -1v)(9 + v)) = 0

Ignore the factor 2.
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 '(9 + v)' equal to zero and attempt to solve:

Simplifying
9 + v = 0

Solving
9 + v = 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 + v = 0 + -9

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

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

Simplifying
v = -9
Solution
v = {3, -9}