2v^2-11v-5=v^2-10v+25

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Solution for 2v^2-11v-5=v^2-10v+25 equation: 


Simplifying
2v2 + -11v + -5 = v2 + -10v + 25

Reorder the terms:
-5 + -11v + 2v2 = v2 + -10v + 25

Reorder the terms:
-5 + -11v + 2v2 = 25 + -10v + v2

Solving
-5 + -11v + 2v2 = 25 + -10v + v2

Solving for variable 'v'.

Reorder the terms:
-5 + -25 + -11v + 10v + 2v2 + -1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

Combine like terms: -5 + -25 = -30
-30 + -11v + 10v + 2v2 + -1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

Combine like terms: -11v + 10v = -1v
-30 + -1v + 2v2 + -1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
-30 + -1v + 1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

Reorder the terms:
-30 + -1v + 1v2 = 25 + -25 + -10v + 10v + v2 + -1v2

Combine like terms: 25 + -25 = 0
-30 + -1v + 1v2 = 0 + -10v + 10v + v2 + -1v2
-30 + -1v + 1v2 = -10v + 10v + v2 + -1v2

Combine like terms: -10v + 10v = 0
-30 + -1v + 1v2 = 0 + v2 + -1v2
-30 + -1v + 1v2 = v2 + -1v2

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