v^2+8v+16=2v^2+10v+13

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Solution for v^2+8v+16=2v^2+10v+13 equation: 


Simplifying
v2 + 8v + 16 = 2v2 + 10v + 13

Reorder the terms:
16 + 8v + v2 = 2v2 + 10v + 13

Reorder the terms:
16 + 8v + v2 = 13 + 10v + 2v2

Solving
16 + 8v + v2 = 13 + 10v + 2v2

Solving for variable 'v'.

Reorder the terms:
16 + -13 + 8v + -10v + v2 + -2v2 = 13 + 10v + 2v2 + -13 + -10v + -2v2

Combine like terms: 16 + -13 = 3
3 + 8v + -10v + v2 + -2v2 = 13 + 10v + 2v2 + -13 + -10v + -2v2

Combine like terms: 8v + -10v = -2v
3 + -2v + v2 + -2v2 = 13 + 10v + 2v2 + -13 + -10v + -2v2

Combine like terms: v2 + -2v2 = -1v2
3 + -2v + -1v2 = 13 + 10v + 2v2 + -13 + -10v + -2v2

Reorder the terms:
3 + -2v + -1v2 = 13 + -13 + 10v + -10v + 2v2 + -2v2

Combine like terms: 13 + -13 = 0
3 + -2v + -1v2 = 0 + 10v + -10v + 2v2 + -2v2
3 + -2v + -1v2 = 10v + -10v + 2v2 + -2v2

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

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

Factor a trinomial.
(1 + -1v)(3 + v) = 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 '(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 = {1, -3}

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