2v^2+17v+39=(v+7)(v+7)

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Solution for 2v^2+17v+39=(v+7)(v+7) equation: 


Simplifying
2v2 + 17v + 39 = (v + 7)(v + 7)

Reorder the terms:
39 + 17v + 2v2 = (v + 7)(v + 7)

Reorder the terms:
39 + 17v + 2v2 = (7 + v)(v + 7)

Reorder the terms:
39 + 17v + 2v2 = (7 + v)(7 + v)

Multiply (7 + v) * (7 + v)
39 + 17v + 2v2 = (7(7 + v) + v(7 + v))
39 + 17v + 2v2 = ((7 * 7 + v * 7) + v(7 + v))
39 + 17v + 2v2 = ((49 + 7v) + v(7 + v))
39 + 17v + 2v2 = (49 + 7v + (7 * v + v * v))
39 + 17v + 2v2 = (49 + 7v + (7v + v2))

Combine like terms: 7v + 7v = 14v
39 + 17v + 2v2 = (49 + 14v + v2)

Solving
39 + 17v + 2v2 = 49 + 14v + v2

Solving for variable 'v'.

Reorder the terms:
39 + -49 + 17v + -14v + 2v2 + -1v2 = 49 + 14v + v2 + -49 + -14v + -1v2

Combine like terms: 39 + -49 = -10
-10 + 17v + -14v + 2v2 + -1v2 = 49 + 14v + v2 + -49 + -14v + -1v2

Combine like terms: 17v + -14v = 3v
-10 + 3v + 2v2 + -1v2 = 49 + 14v + v2 + -49 + -14v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
-10 + 3v + 1v2 = 49 + 14v + v2 + -49 + -14v + -1v2

Reorder the terms:
-10 + 3v + 1v2 = 49 + -49 + 14v + -14v + v2 + -1v2

Combine like terms: 49 + -49 = 0
-10 + 3v + 1v2 = 0 + 14v + -14v + v2 + -1v2
-10 + 3v + 1v2 = 14v + -14v + v2 + -1v2

Combine like terms: 14v + -14v = 0
-10 + 3v + 1v2 = 0 + v2 + -1v2
-10 + 3v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
-10 + 3v + 1v2 = 0

Factor a trinomial.
(-5 + -1v)(2 + -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 '(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 = {-5, 2}

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