5v^2-31v=-2v-20

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Solution for 5v^2-31v=-2v-20 equation: 


Simplifying
5v2 + -31v = -2v + -20

Reorder the terms:
-31v + 5v2 = -2v + -20

Reorder the terms:
-31v + 5v2 = -20 + -2v

Solving
-31v + 5v2 = -20 + -2v

Solving for variable 'v'.

Reorder the terms:
20 + -31v + 2v + 5v2 = -20 + -2v + 20 + 2v

Combine like terms: -31v + 2v = -29v
20 + -29v + 5v2 = -20 + -2v + 20 + 2v

Reorder the terms:
20 + -29v + 5v2 = -20 + 20 + -2v + 2v

Combine like terms: -20 + 20 = 0
20 + -29v + 5v2 = 0 + -2v + 2v
20 + -29v + 5v2 = -2v + 2v

Combine like terms: -2v + 2v = 0
20 + -29v + 5v2 = 0

Factor a trinomial.
(4 + -5v)(5 + -1v) = 0


Subproblem 1
Set the factor '(4 + -5v)' equal to zero and attempt to solve:

Simplifying
4 + -5v = 0

Solving
4 + -5v = 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 + -5v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5v = 0 + -4
-5v = 0 + -4

Combine like terms: 0 + -4 = -4
-5v = -4

Divide each side by '-5'.
v = 0.8

Simplifying
v = 0.8

Subproblem 2
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 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 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5
Solution
v = {0.8, 5}

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