2v^2-19v+46=v^2-8v+16

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Solution for 2v^2-19v+46=v^2-8v+16 equation: 


Simplifying
2v2 + -19v + 46 = v2 + -8v + 16

Reorder the terms:
46 + -19v + 2v2 = v2 + -8v + 16

Reorder the terms:
46 + -19v + 2v2 = 16 + -8v + v2

Solving
46 + -19v + 2v2 = 16 + -8v + v2

Solving for variable 'v'.

Reorder the terms:
46 + -16 + -19v + 8v + 2v2 + -1v2 = 16 + -8v + v2 + -16 + 8v + -1v2

Combine like terms: 46 + -16 = 30
30 + -19v + 8v + 2v2 + -1v2 = 16 + -8v + v2 + -16 + 8v + -1v2

Combine like terms: -19v + 8v = -11v
30 + -11v + 2v2 + -1v2 = 16 + -8v + v2 + -16 + 8v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
30 + -11v + 1v2 = 16 + -8v + v2 + -16 + 8v + -1v2

Reorder the terms:
30 + -11v + 1v2 = 16 + -16 + -8v + 8v + v2 + -1v2

Combine like terms: 16 + -16 = 0
30 + -11v + 1v2 = 0 + -8v + 8v + v2 + -1v2
30 + -11v + 1v2 = -8v + 8v + v2 + -1v2

Combine like terms: -8v + 8v = 0
30 + -11v + 1v2 = 0 + v2 + -1v2
30 + -11v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
30 + -11v + 1v2 = 0

Factor a trinomial.
(5 + -1v)(6 + -1v) = 0


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

Simplifying
5 + -1v = 0

Solving
5 + -1v = 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 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5

Subproblem 2
Set the factor '(6 + -1v)' equal to zero and attempt to solve:

Simplifying
6 + -1v = 0

Solving
6 + -1v = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1v = 0 + -6

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

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

Divide each side by '-1'.
v = 6

Simplifying
v = 6
Solution
v = {5, 6}

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