2v^2-6v+45=v^2-12v+36

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Solution for 2v^2-6v+45=v^2-12v+36 equation: 


Simplifying
2v2 + -6v + 45 = v2 + -12v + 36

Reorder the terms:
45 + -6v + 2v2 = v2 + -12v + 36

Reorder the terms:
45 + -6v + 2v2 = 36 + -12v + v2

Solving
45 + -6v + 2v2 = 36 + -12v + v2

Solving for variable 'v'.

Reorder the terms:
45 + -36 + -6v + 12v + 2v2 + -1v2 = 36 + -12v + v2 + -36 + 12v + -1v2

Combine like terms: 45 + -36 = 9
9 + -6v + 12v + 2v2 + -1v2 = 36 + -12v + v2 + -36 + 12v + -1v2

Combine like terms: -6v + 12v = 6v
9 + 6v + 2v2 + -1v2 = 36 + -12v + v2 + -36 + 12v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
9 + 6v + 1v2 = 36 + -12v + v2 + -36 + 12v + -1v2

Reorder the terms:
9 + 6v + 1v2 = 36 + -36 + -12v + 12v + v2 + -1v2

Combine like terms: 36 + -36 = 0
9 + 6v + 1v2 = 0 + -12v + 12v + v2 + -1v2
9 + 6v + 1v2 = -12v + 12v + v2 + -1v2

Combine like terms: -12v + 12v = 0
9 + 6v + 1v2 = 0 + v2 + -1v2
9 + 6v + 1v2 = v2 + -1v2

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

Factor a trinomial.
(3 + v)(3 + v) = 0


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

Simplifying
3 + v = 0

Solving
3 + v = 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 + v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + v = 0 + -3
v = 0 + -3

Combine like terms: 0 + -3 = -3
v = -3

Simplifying
v = -3

Subproblem 2
Set the factor '(3 + v)' equal to zero and attempt to solve:

Simplifying
3 + v = 0

Solving
3 + v = 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 + v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + v = 0 + -3
v = 0 + -3

Combine like terms: 0 + -3 = -3
v = -3

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

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