((2v^2)-3v-1)=(v^2)+9

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Solution for ((2v^2)-3v-1)=(v^2)+9 equation: 


Simplifying
((2v2) + -3v + -1) = (v2) + 9

Reorder the terms:
(-1 + -3v + (2v2)) = (v2) + 9

Remove parenthesis around (-1 + -3v + (2v2))
-1 + -3v + (2v2) = (v2) + 9
-1 + -3v + (2v2) = v2 + 9

Reorder the terms:
-1 + -3v + (2v2) = 9 + v2

Solving
-1 + -3v + (2v2) = 9 + v2

Solving for variable 'v'.

Reorder the terms:
-1 + -9 + -3v + (2v2) + -1v2 = 9 + v2 + -9 + -1v2

Combine like terms: -1 + -9 = -10
-10 + -3v + (2v2) + -1v2 = 9 + v2 + -9 + -1v2

Combine like terms: (2v2) + -1v2 = 1v2
-10 + -3v + 1v2 = 9 + v2 + -9 + -1v2

Reorder the terms:
-10 + -3v + 1v2 = 9 + -9 + v2 + -1v2

Combine like terms: 9 + -9 = 0
-10 + -3v + 1v2 = 0 + v2 + -1v2
-10 + -3v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
-10 + -3v + 1v2 = 0

Factor a trinomial.
(-2 + -1v)(5 + -1v) = 0


Subproblem 1
Set the factor '(-2 + -1v)' equal to zero and attempt to solve:

Simplifying
-2 + -1v = 0

Solving
-2 + -1v = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1v = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1v = 0 + 2
-1v = 0 + 2

Combine like terms: 0 + 2 = 2
-1v = 2

Divide each side by '-1'.
v = -2

Simplifying
v = -2

Subproblem 2
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
Solution
v = {-2, 5}

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