(v-7)(v-7)=2v^2-20v+54

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Solution for (v-7)(v-7)=2v^2-20v+54 equation: 


Simplifying
(v + -7)(v + -7) = 2v2 + -20v + 54

Reorder the terms:
(-7 + v)(v + -7) = 2v2 + -20v + 54

Reorder the terms:
(-7 + v)(-7 + v) = 2v2 + -20v + 54

Multiply (-7 + v) * (-7 + v)
(-7(-7 + v) + v(-7 + v)) = 2v2 + -20v + 54
((-7 * -7 + v * -7) + v(-7 + v)) = 2v2 + -20v + 54
((49 + -7v) + v(-7 + v)) = 2v2 + -20v + 54
(49 + -7v + (-7 * v + v * v)) = 2v2 + -20v + 54
(49 + -7v + (-7v + v2)) = 2v2 + -20v + 54

Combine like terms: -7v + -7v = -14v
(49 + -14v + v2) = 2v2 + -20v + 54

Reorder the terms:
49 + -14v + v2 = 54 + -20v + 2v2

Solving
49 + -14v + v2 = 54 + -20v + 2v2

Solving for variable 'v'.

Reorder the terms:
49 + -54 + -14v + 20v + v2 + -2v2 = 54 + -20v + 2v2 + -54 + 20v + -2v2

Combine like terms: 49 + -54 = -5
-5 + -14v + 20v + v2 + -2v2 = 54 + -20v + 2v2 + -54 + 20v + -2v2

Combine like terms: -14v + 20v = 6v
-5 + 6v + v2 + -2v2 = 54 + -20v + 2v2 + -54 + 20v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-5 + 6v + -1v2 = 54 + -20v + 2v2 + -54 + 20v + -2v2

Reorder the terms:
-5 + 6v + -1v2 = 54 + -54 + -20v + 20v + 2v2 + -2v2

Combine like terms: 54 + -54 = 0
-5 + 6v + -1v2 = 0 + -20v + 20v + 2v2 + -2v2
-5 + 6v + -1v2 = -20v + 20v + 2v2 + -2v2

Combine like terms: -20v + 20v = 0
-5 + 6v + -1v2 = 0 + 2v2 + -2v2
-5 + 6v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-5 + 6v + -1v2 = 0

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


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

Simplifying
-5 + v = 0

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

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

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

Simplifying
v = 5

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

Simplifying
1 + -1v = 0

Solving
1 + -1v = 0

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

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

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

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

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

Simplifying
v = 1
Solution
v = {5, 1}

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