2v^2-15v+47=(v-7)(v-7)

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Solution for 2v^2-15v+47=(v-7)(v-7) equation: 


Simplifying
2v2 + -15v + 47 = (v + -7)(v + -7)

Reorder the terms:
47 + -15v + 2v2 = (v + -7)(v + -7)

Reorder the terms:
47 + -15v + 2v2 = (-7 + v)(v + -7)

Reorder the terms:
47 + -15v + 2v2 = (-7 + v)(-7 + v)

Multiply (-7 + v) * (-7 + v)
47 + -15v + 2v2 = (-7(-7 + v) + v(-7 + v))
47 + -15v + 2v2 = ((-7 * -7 + v * -7) + v(-7 + v))
47 + -15v + 2v2 = ((49 + -7v) + v(-7 + v))
47 + -15v + 2v2 = (49 + -7v + (-7 * v + v * v))
47 + -15v + 2v2 = (49 + -7v + (-7v + v2))

Combine like terms: -7v + -7v = -14v
47 + -15v + 2v2 = (49 + -14v + v2)

Solving
47 + -15v + 2v2 = 49 + -14v + v2

Solving for variable 'v'.

Reorder the terms:
47 + -49 + -15v + 14v + 2v2 + -1v2 = 49 + -14v + v2 + -49 + 14v + -1v2

Combine like terms: 47 + -49 = -2
-2 + -15v + 14v + 2v2 + -1v2 = 49 + -14v + v2 + -49 + 14v + -1v2

Combine like terms: -15v + 14v = -1v
-2 + -1v + 2v2 + -1v2 = 49 + -14v + v2 + -49 + 14v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
-2 + -1v + 1v2 = 49 + -14v + v2 + -49 + 14v + -1v2

Reorder the terms:
-2 + -1v + 1v2 = 49 + -49 + -14v + 14v + v2 + -1v2

Combine like terms: 49 + -49 = 0
-2 + -1v + 1v2 = 0 + -14v + 14v + v2 + -1v2
-2 + -1v + 1v2 = -14v + 14v + v2 + -1v2

Combine like terms: -14v + 14v = 0
-2 + -1v + 1v2 = 0 + v2 + -1v2
-2 + -1v + 1v2 = v2 + -1v2

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

Factor a trinomial.
(-1 + -1v)(2 + -1v) = 0


Subproblem 1
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

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

Simplifying
2 + -1v = 0

Solving
2 + -1v = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1v = 0 + -2
-1v = 0 + -2

Combine like terms: 0 + -2 = -2
-1v = -2

Divide each side by '-1'.
v = 2

Simplifying
v = 2
Solution
v = {-1, 2}

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