2v^2+4v+34=v^2-6v+9

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Solution for 2v^2+4v+34=v^2-6v+9 equation: 


Simplifying
2v2 + 4v + 34 = v2 + -6v + 9

Reorder the terms:
34 + 4v + 2v2 = v2 + -6v + 9

Reorder the terms:
34 + 4v + 2v2 = 9 + -6v + v2

Solving
34 + 4v + 2v2 = 9 + -6v + v2

Solving for variable 'v'.

Reorder the terms:
34 + -9 + 4v + 6v + 2v2 + -1v2 = 9 + -6v + v2 + -9 + 6v + -1v2

Combine like terms: 34 + -9 = 25
25 + 4v + 6v + 2v2 + -1v2 = 9 + -6v + v2 + -9 + 6v + -1v2

Combine like terms: 4v + 6v = 10v
25 + 10v + 2v2 + -1v2 = 9 + -6v + v2 + -9 + 6v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
25 + 10v + 1v2 = 9 + -6v + v2 + -9 + 6v + -1v2

Reorder the terms:
25 + 10v + 1v2 = 9 + -9 + -6v + 6v + v2 + -1v2

Combine like terms: 9 + -9 = 0
25 + 10v + 1v2 = 0 + -6v + 6v + v2 + -1v2
25 + 10v + 1v2 = -6v + 6v + v2 + -1v2

Combine like terms: -6v + 6v = 0
25 + 10v + 1v2 = 0 + v2 + -1v2
25 + 10v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
25 + 10v + 1v2 = 0

Factor a trinomial.
(5 + v)(5 + v) = 0


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

Simplifying
5 + v = 0

Solving
5 + v = 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 + v = 0 + -5

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

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

Simplifying
v = -5

Subproblem 2
Set the factor '(5 + v)' equal to zero and attempt to solve:

Simplifying
5 + v = 0

Solving
5 + v = 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 + v = 0 + -5

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

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

Simplifying
v = -5
Solution
v = {-5, -5}

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