v^2-3v+3v-9+v^2-2v-3v+6-v^2+2v-5v+10=0

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Solution for v^2-3v+3v-9+v^2-2v-3v+6-v^2+2v-5v+10=0 equation: 


Simplifying
v2 + -3v + 3v + -9 + v2 + -2v + -3v + 6 + -1v2 + 2v + -5v + 10 = 0

Reorder the terms:
-9 + 6 + 10 + -3v + 3v + -2v + -3v + 2v + -5v + v2 + v2 + -1v2 = 0

Combine like terms: -9 + 6 = -3
-3 + 10 + -3v + 3v + -2v + -3v + 2v + -5v + v2 + v2 + -1v2 = 0

Combine like terms: -3 + 10 = 7
7 + -3v + 3v + -2v + -3v + 2v + -5v + v2 + v2 + -1v2 = 0

Combine like terms: -3v + 3v = 0
7 + 0 + -2v + -3v + 2v + -5v + v2 + v2 + -1v2 = 0
7 + -2v + -3v + 2v + -5v + v2 + v2 + -1v2 = 0

Combine like terms: -2v + -3v = -5v
7 + -5v + 2v + -5v + v2 + v2 + -1v2 = 0

Combine like terms: -5v + 2v = -3v
7 + -3v + -5v + v2 + v2 + -1v2 = 0

Combine like terms: -3v + -5v = -8v
7 + -8v + v2 + v2 + -1v2 = 0

Combine like terms: v2 + v2 = 2v2
7 + -8v + 2v2 + -1v2 = 0

Combine like terms: 2v2 + -1v2 = 1v2
7 + -8v + 1v2 = 0

Solving
7 + -8v + 1v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(1 + -1v)(7 + -1v) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1v = 0 + -7
-1v = 0 + -7

Combine like terms: 0 + -7 = -7
-1v = -7

Divide each side by '-1'.
v = 7

Simplifying
v = 7
Solution
v = {1, 7}

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