v^2-3v-17=-9-5v

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Solution for v^2-3v-17=-9-5v equation: 


Simplifying
v2 + -3v + -17 = -9 + -5v

Reorder the terms:
-17 + -3v + v2 = -9 + -5v

Solving
-17 + -3v + v2 = -9 + -5v

Solving for variable 'v'.

Reorder the terms:
-17 + 9 + -3v + 5v + v2 = -9 + -5v + 9 + 5v

Combine like terms: -17 + 9 = -8
-8 + -3v + 5v + v2 = -9 + -5v + 9 + 5v

Combine like terms: -3v + 5v = 2v
-8 + 2v + v2 = -9 + -5v + 9 + 5v

Reorder the terms:
-8 + 2v + v2 = -9 + 9 + -5v + 5v

Combine like terms: -9 + 9 = 0
-8 + 2v + v2 = 0 + -5v + 5v
-8 + 2v + v2 = -5v + 5v

Combine like terms: -5v + 5v = 0
-8 + 2v + v2 = 0

Factor a trinomial.
(-4 + -1v)(2 + -1v) = 0


Subproblem 1
Set the factor '(-4 + -1v)' equal to zero and attempt to solve:

Simplifying
-4 + -1v = 0

Solving
-4 + -1v = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1v = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1v = 0 + 4
-1v = 0 + 4

Combine like terms: 0 + 4 = 4
-1v = 4

Divide each side by '-1'.
v = -4

Simplifying
v = -4

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 = {-4, 2}

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