v^2-5v=2v+18

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Solution for v^2-5v=2v+18 equation: 


Simplifying
v2 + -5v = 2v + 18

Reorder the terms:
-5v + v2 = 2v + 18

Reorder the terms:
-5v + v2 = 18 + 2v

Solving
-5v + v2 = 18 + 2v

Solving for variable 'v'.

Reorder the terms:
-18 + -5v + -2v + v2 = 18 + 2v + -18 + -2v

Combine like terms: -5v + -2v = -7v
-18 + -7v + v2 = 18 + 2v + -18 + -2v

Reorder the terms:
-18 + -7v + v2 = 18 + -18 + 2v + -2v

Combine like terms: 18 + -18 = 0
-18 + -7v + v2 = 0 + 2v + -2v
-18 + -7v + v2 = 2v + -2v

Combine like terms: 2v + -2v = 0
-18 + -7v + v2 = 0

Factor a trinomial.
(-2 + -1v)(9 + -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 '(9 + -1v)' equal to zero and attempt to solve:

Simplifying
9 + -1v = 0

Solving
9 + -1v = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1v = 0 + -9

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

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

Divide each side by '-1'.
v = 9

Simplifying
v = 9
Solution
v = {-2, 9}

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