3v^2+2v=24+v

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Solution for 3v^2+2v=24+v equation: 


Simplifying
3v2 + 2v = 24 + v

Reorder the terms:
2v + 3v2 = 24 + v

Solving
2v + 3v2 = 24 + v

Solving for variable 'v'.

Reorder the terms:
-24 + 2v + -1v + 3v2 = 24 + v + -24 + -1v

Combine like terms: 2v + -1v = 1v
-24 + 1v + 3v2 = 24 + v + -24 + -1v

Reorder the terms:
-24 + 1v + 3v2 = 24 + -24 + v + -1v

Combine like terms: 24 + -24 = 0
-24 + 1v + 3v2 = 0 + v + -1v
-24 + 1v + 3v2 = v + -1v

Combine like terms: v + -1v = 0
-24 + 1v + 3v2 = 0

Factor a trinomial.
(-3 + -1v)(8 + -3v) = 0


Subproblem 1
Set the factor '(-3 + -1v)' equal to zero and attempt to solve:

Simplifying
-3 + -1v = 0

Solving
-3 + -1v = 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 + -1v = 0 + 3

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

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

Divide each side by '-1'.
v = -3

Simplifying
v = -3

Subproblem 2
Set the factor '(8 + -3v)' equal to zero and attempt to solve:

Simplifying
8 + -3v = 0

Solving
8 + -3v = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3v = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3v = 0 + -8
-3v = 0 + -8

Combine like terms: 0 + -8 = -8
-3v = -8

Divide each side by '-3'.
v = 2.666666667

Simplifying
v = 2.666666667
Solution
v = {-3, 2.666666667}

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