2v^2+9v+5=v^2+6v+9

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Solution for 2v^2+9v+5=v^2+6v+9 equation: 


Simplifying
2v2 + 9v + 5 = v2 + 6v + 9

Reorder the terms:
5 + 9v + 2v2 = v2 + 6v + 9

Reorder the terms:
5 + 9v + 2v2 = 9 + 6v + v2

Solving
5 + 9v + 2v2 = 9 + 6v + v2

Solving for variable 'v'.

Reorder the terms:
5 + -9 + 9v + -6v + 2v2 + -1v2 = 9 + 6v + v2 + -9 + -6v + -1v2

Combine like terms: 5 + -9 = -4
-4 + 9v + -6v + 2v2 + -1v2 = 9 + 6v + v2 + -9 + -6v + -1v2

Combine like terms: 9v + -6v = 3v
-4 + 3v + 2v2 + -1v2 = 9 + 6v + v2 + -9 + -6v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
-4 + 3v + 1v2 = 9 + 6v + v2 + -9 + -6v + -1v2

Reorder the terms:
-4 + 3v + 1v2 = 9 + -9 + 6v + -6v + v2 + -1v2

Combine like terms: 9 + -9 = 0
-4 + 3v + 1v2 = 0 + 6v + -6v + v2 + -1v2
-4 + 3v + 1v2 = 6v + -6v + v2 + -1v2

Combine like terms: 6v + -6v = 0
-4 + 3v + 1v2 = 0 + v2 + -1v2
-4 + 3v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
-4 + 3v + 1v2 = 0

Factor a trinomial.
(-4 + -1v)(1 + -1v) = 0


Subproblem 1
Set the factor '(-4 + -1v)' equal to zero and attempt to solve:

Simplifying
-4 + -1v = 0

Solving
-4 + -1v = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1v = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1v = 0 + 4
-1v = 0 + 4

Combine like terms: 0 + 4 = 4
-1v = 4

Divide each side by '-1'.
v = -4

Simplifying
v = -4

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

Simplifying
1 + -1v = 0

Solving
1 + -1v = 0

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

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

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

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

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

Simplifying
v = 1
Solution
v = {-4, 1}

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