2v^2-21v+55=(v-5)(v-5)

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Solution for 2v^2-21v+55=(v-5)(v-5) equation: 


Simplifying
2v2 + -21v + 55 = (v + -5)(v + -5)

Reorder the terms:
55 + -21v + 2v2 = (v + -5)(v + -5)

Reorder the terms:
55 + -21v + 2v2 = (-5 + v)(v + -5)

Reorder the terms:
55 + -21v + 2v2 = (-5 + v)(-5 + v)

Multiply (-5 + v) * (-5 + v)
55 + -21v + 2v2 = (-5(-5 + v) + v(-5 + v))
55 + -21v + 2v2 = ((-5 * -5 + v * -5) + v(-5 + v))
55 + -21v + 2v2 = ((25 + -5v) + v(-5 + v))
55 + -21v + 2v2 = (25 + -5v + (-5 * v + v * v))
55 + -21v + 2v2 = (25 + -5v + (-5v + v2))

Combine like terms: -5v + -5v = -10v
55 + -21v + 2v2 = (25 + -10v + v2)

Solving
55 + -21v + 2v2 = 25 + -10v + v2

Solving for variable 'v'.

Reorder the terms:
55 + -25 + -21v + 10v + 2v2 + -1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

Combine like terms: 55 + -25 = 30
30 + -21v + 10v + 2v2 + -1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

Combine like terms: -21v + 10v = -11v
30 + -11v + 2v2 + -1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

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

Reorder the terms:
30 + -11v + 1v2 = 25 + -25 + -10v + 10v + v2 + -1v2

Combine like terms: 25 + -25 = 0
30 + -11v + 1v2 = 0 + -10v + 10v + v2 + -1v2
30 + -11v + 1v2 = -10v + 10v + v2 + -1v2

Combine like terms: -10v + 10v = 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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