2v^2+9v+5=v^2+10v+25

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Solution for 2v^2+9v+5=v^2+10v+25 equation: 


Simplifying
2v2 + 9v + 5 = v2 + 10v + 25

Reorder the terms:
5 + 9v + 2v2 = v2 + 10v + 25

Reorder the terms:
5 + 9v + 2v2 = 25 + 10v + v2

Solving
5 + 9v + 2v2 = 25 + 10v + v2

Solving for variable 'v'.

Reorder the terms:
5 + -25 + 9v + -10v + 2v2 + -1v2 = 25 + 10v + v2 + -25 + -10v + -1v2

Combine like terms: 5 + -25 = -20
-20 + 9v + -10v + 2v2 + -1v2 = 25 + 10v + v2 + -25 + -10v + -1v2

Combine like terms: 9v + -10v = -1v
-20 + -1v + 2v2 + -1v2 = 25 + 10v + v2 + -25 + -10v + -1v2

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

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

Combine like terms: 25 + -25 = 0
-20 + -1v + 1v2 = 0 + 10v + -10v + v2 + -1v2
-20 + -1v + 1v2 = 10v + -10v + v2 + -1v2

Combine like terms: 10v + -10v = 0
-20 + -1v + 1v2 = 0 + v2 + -1v2
-20 + -1v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
-20 + -1v + 1v2 = 0

Factor a trinomial.
(-4 + -1v)(5 + -1v) = 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 '(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
Solution
v = {-4, 5}

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