(v-5)(v-5)=2v^2-9v+19

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Solution for (v-5)(v-5)=2v^2-9v+19 equation: 


Simplifying
(v + -5)(v + -5) = 2v2 + -9v + 19

Reorder the terms:
(-5 + v)(v + -5) = 2v2 + -9v + 19

Reorder the terms:
(-5 + v)(-5 + v) = 2v2 + -9v + 19

Multiply (-5 + v) * (-5 + v)
(-5(-5 + v) + v(-5 + v)) = 2v2 + -9v + 19
((-5 * -5 + v * -5) + v(-5 + v)) = 2v2 + -9v + 19
((25 + -5v) + v(-5 + v)) = 2v2 + -9v + 19
(25 + -5v + (-5 * v + v * v)) = 2v2 + -9v + 19
(25 + -5v + (-5v + v2)) = 2v2 + -9v + 19

Combine like terms: -5v + -5v = -10v
(25 + -10v + v2) = 2v2 + -9v + 19

Reorder the terms:
25 + -10v + v2 = 19 + -9v + 2v2

Solving
25 + -10v + v2 = 19 + -9v + 2v2

Solving for variable 'v'.

Reorder the terms:
25 + -19 + -10v + 9v + v2 + -2v2 = 19 + -9v + 2v2 + -19 + 9v + -2v2

Combine like terms: 25 + -19 = 6
6 + -10v + 9v + v2 + -2v2 = 19 + -9v + 2v2 + -19 + 9v + -2v2

Combine like terms: -10v + 9v = -1v
6 + -1v + v2 + -2v2 = 19 + -9v + 2v2 + -19 + 9v + -2v2

Combine like terms: v2 + -2v2 = -1v2
6 + -1v + -1v2 = 19 + -9v + 2v2 + -19 + 9v + -2v2

Reorder the terms:
6 + -1v + -1v2 = 19 + -19 + -9v + 9v + 2v2 + -2v2

Combine like terms: 19 + -19 = 0
6 + -1v + -1v2 = 0 + -9v + 9v + 2v2 + -2v2
6 + -1v + -1v2 = -9v + 9v + 2v2 + -2v2

Combine like terms: -9v + 9v = 0
6 + -1v + -1v2 = 0 + 2v2 + -2v2
6 + -1v + -1v2 = 2v2 + -2v2

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

Factor a trinomial.
(2 + -1v)(3 + v) = 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 '(3 + v)' equal to zero and attempt to solve:

Simplifying
3 + v = 0

Solving
3 + v = 0

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

Add '-3' to each side of the equation.
3 + -3 + v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + v = 0 + -3
v = 0 + -3

Combine like terms: 0 + -3 = -3
v = -3

Simplifying
v = -3
Solution
v = {2, -3}

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