2v^2-19v+39=(v-5)(v-5)

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Solution for 2v^2-19v+39=(v-5)(v-5) equation: 


Simplifying
2v2 + -19v + 39 = (v + -5)(v + -5)

Reorder the terms:
39 + -19v + 2v2 = (v + -5)(v + -5)

Reorder the terms:
39 + -19v + 2v2 = (-5 + v)(v + -5)

Reorder the terms:
39 + -19v + 2v2 = (-5 + v)(-5 + v)

Multiply (-5 + v) * (-5 + v)
39 + -19v + 2v2 = (-5(-5 + v) + v(-5 + v))
39 + -19v + 2v2 = ((-5 * -5 + v * -5) + v(-5 + v))
39 + -19v + 2v2 = ((25 + -5v) + v(-5 + v))
39 + -19v + 2v2 = (25 + -5v + (-5 * v + v * v))
39 + -19v + 2v2 = (25 + -5v + (-5v + v2))

Combine like terms: -5v + -5v = -10v
39 + -19v + 2v2 = (25 + -10v + v2)

Solving
39 + -19v + 2v2 = 25 + -10v + v2

Solving for variable 'v'.

Reorder the terms:
39 + -25 + -19v + 10v + 2v2 + -1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

Combine like terms: 39 + -25 = 14
14 + -19v + 10v + 2v2 + -1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

Combine like terms: -19v + 10v = -9v
14 + -9v + 2v2 + -1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
14 + -9v + 1v2 = 25 + -10v + v2 + -25 + 10v + -1v2

Reorder the terms:
14 + -9v + 1v2 = 25 + -25 + -10v + 10v + v2 + -1v2

Combine like terms: 25 + -25 = 0
14 + -9v + 1v2 = 0 + -10v + 10v + v2 + -1v2
14 + -9v + 1v2 = -10v + 10v + v2 + -1v2

Combine like terms: -10v + 10v = 0
14 + -9v + 1v2 = 0 + v2 + -1v2
14 + -9v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
14 + -9v + 1v2 = 0

Factor a trinomial.
(2 + -1v)(7 + -1v) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1v = 0 + -7
-1v = 0 + -7

Combine like terms: 0 + -7 = -7
-1v = -7

Divide each side by '-1'.
v = 7

Simplifying
v = 7
Solution
v = {2, 7}

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