2v^2-20v+46=v^2-10v+25

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Solution for 2v^2-20v+46=v^2-10v+25 equation: 


Simplifying
2v2 + -20v + 46 = v2 + -10v + 25

Reorder the terms:
46 + -20v + 2v2 = v2 + -10v + 25

Reorder the terms:
46 + -20v + 2v2 = 25 + -10v + v2

Solving
46 + -20v + 2v2 = 25 + -10v + v2

Solving for variable 'v'.

Reorder the terms:
46 + -25 + -20v + 10v + 2v2 + -1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

Combine like terms: 46 + -25 = 21
21 + -20v + 10v + 2v2 + -1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

Combine like terms: -20v + 10v = -10v
21 + -10v + 2v2 + -1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
21 + -10v + 1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

Reorder the terms:
21 + -10v + 1v2 = 25 + -25 + -10v + 10v + v2 + -1v2

Combine like terms: 25 + -25 = 0
21 + -10v + 1v2 = 0 + -10v + 10v + v2 + -1v2
21 + -10v + 1v2 = -10v + 10v + v2 + -1v2

Combine like terms: -10v + 10v = 0
21 + -10v + 1v2 = 0 + v2 + -1v2
21 + -10v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
21 + -10v + 1v2 = 0

Factor a trinomial.
(3 + -1v)(7 + -1v) = 0


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

Simplifying
3 + -1v = 0

Solving
3 + -1v = 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 + -1v = 0 + -3

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

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

Divide each side by '-1'.
v = 3

Simplifying
v = 3

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 = {3, 7}

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