v^2-33v+90=-2v^2

Solution for v^2-33v+90=-2v^2 equation:

Simplifying
v2 + -33v + 90 = -2v2

Reorder the terms:
90 + -33v + v2 = -2v2

Solving
90 + -33v + v2 = -2v2

Solving for variable 'v'.

Combine like terms: v2 + 2v2 = 3v2
90 + -33v + 3v2 = -2v2 + 2v2

Combine like terms: -2v2 + 2v2 = 0
90 + -33v + 3v2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(30 + -11v + v2) = 0

Factor a trinomial.
3((5 + -1v)(6 + -1v)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 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 = {5, 6}