v^2+10v+25=2v^2+8v+17

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Solution for v^2+10v+25=2v^2+8v+17 equation: 


Simplifying
v2 + 10v + 25 = 2v2 + 8v + 17

Reorder the terms:
25 + 10v + v2 = 2v2 + 8v + 17

Reorder the terms:
25 + 10v + v2 = 17 + 8v + 2v2

Solving
25 + 10v + v2 = 17 + 8v + 2v2

Solving for variable 'v'.

Reorder the terms:
25 + -17 + 10v + -8v + v2 + -2v2 = 17 + 8v + 2v2 + -17 + -8v + -2v2

Combine like terms: 25 + -17 = 8
8 + 10v + -8v + v2 + -2v2 = 17 + 8v + 2v2 + -17 + -8v + -2v2

Combine like terms: 10v + -8v = 2v
8 + 2v + v2 + -2v2 = 17 + 8v + 2v2 + -17 + -8v + -2v2

Combine like terms: v2 + -2v2 = -1v2
8 + 2v + -1v2 = 17 + 8v + 2v2 + -17 + -8v + -2v2

Reorder the terms:
8 + 2v + -1v2 = 17 + -17 + 8v + -8v + 2v2 + -2v2

Combine like terms: 17 + -17 = 0
8 + 2v + -1v2 = 0 + 8v + -8v + 2v2 + -2v2
8 + 2v + -1v2 = 8v + -8v + 2v2 + -2v2

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

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

Factor a trinomial.
(4 + -1v)(2 + v) = 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 '(2 + v)' equal to zero and attempt to solve:

Simplifying
2 + v = 0

Solving
2 + v = 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 + v = 0 + -2

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

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

Simplifying
v = -2
Solution
v = {4, -2}

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