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

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


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

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

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

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

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

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

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

Solving for variable 'v'.

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

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

Combine like terms: -10v + 19v = 9v
-14 + 9v + v2 + -2v2 = 39 + -19v + 2v2 + -39 + 19v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-14 + 9v + -1v2 = 39 + -19v + 2v2 + -39 + 19v + -2v2

Reorder the terms:
-14 + 9v + -1v2 = 39 + -39 + -19v + 19v + 2v2 + -2v2

Combine like terms: 39 + -39 = 0
-14 + 9v + -1v2 = 0 + -19v + 19v + 2v2 + -2v2
-14 + 9v + -1v2 = -19v + 19v + 2v2 + -2v2

Combine like terms: -19v + 19v = 0
-14 + 9v + -1v2 = 0 + 2v2 + -2v2
-14 + 9v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-14 + 9v + -1v2 = 0

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


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

Simplifying
-7 + v = 0

Solving
-7 + v = 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 + v = 0 + 7

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

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

Simplifying
v = 7

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 = {7, 2}

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