-2v^2+23v+42=-5v^2+2

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Solution for -2v^2+23v+42=-5v^2+2 equation: 


Simplifying
-2v2 + 23v + 42 = -5v2 + 2

Reorder the terms:
42 + 23v + -2v2 = -5v2 + 2

Reorder the terms:
42 + 23v + -2v2 = 2 + -5v2

Solving
42 + 23v + -2v2 = 2 + -5v2

Solving for variable 'v'.

Reorder the terms:
42 + -2 + 23v + -2v2 + 5v2 = 2 + -5v2 + -2 + 5v2

Combine like terms: 42 + -2 = 40
40 + 23v + -2v2 + 5v2 = 2 + -5v2 + -2 + 5v2

Combine like terms: -2v2 + 5v2 = 3v2
40 + 23v + 3v2 = 2 + -5v2 + -2 + 5v2

Reorder the terms:
40 + 23v + 3v2 = 2 + -2 + -5v2 + 5v2

Combine like terms: 2 + -2 = 0
40 + 23v + 3v2 = 0 + -5v2 + 5v2
40 + 23v + 3v2 = -5v2 + 5v2

Combine like terms: -5v2 + 5v2 = 0
40 + 23v + 3v2 = 0

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


Subproblem 1
Set the factor '(5 + v)' equal to zero and attempt to solve:

Simplifying
5 + v = 0

Solving
5 + v = 0

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

Add '-5' to each side of the equation.
5 + -5 + v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + v = 0 + -5
v = 0 + -5

Combine like terms: 0 + -5 = -5
v = -5

Simplifying
v = -5

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 = {-5, -2.666666667}

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