8v^2-21v+5=-4v+6v^2-3

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Solution for 8v^2-21v+5=-4v+6v^2-3 equation: 


Simplifying
8v2 + -21v + 5 = -4v + 6v2 + -3

Reorder the terms:
5 + -21v + 8v2 = -4v + 6v2 + -3

Reorder the terms:
5 + -21v + 8v2 = -3 + -4v + 6v2

Solving
5 + -21v + 8v2 = -3 + -4v + 6v2

Solving for variable 'v'.

Reorder the terms:
5 + 3 + -21v + 4v + 8v2 + -6v2 = -3 + -4v + 6v2 + 3 + 4v + -6v2

Combine like terms: 5 + 3 = 8
8 + -21v + 4v + 8v2 + -6v2 = -3 + -4v + 6v2 + 3 + 4v + -6v2

Combine like terms: -21v + 4v = -17v
8 + -17v + 8v2 + -6v2 = -3 + -4v + 6v2 + 3 + 4v + -6v2

Combine like terms: 8v2 + -6v2 = 2v2
8 + -17v + 2v2 = -3 + -4v + 6v2 + 3 + 4v + -6v2

Reorder the terms:
8 + -17v + 2v2 = -3 + 3 + -4v + 4v + 6v2 + -6v2

Combine like terms: -3 + 3 = 0
8 + -17v + 2v2 = 0 + -4v + 4v + 6v2 + -6v2
8 + -17v + 2v2 = -4v + 4v + 6v2 + -6v2

Combine like terms: -4v + 4v = 0
8 + -17v + 2v2 = 0 + 6v2 + -6v2
8 + -17v + 2v2 = 6v2 + -6v2

Combine like terms: 6v2 + -6v2 = 0
8 + -17v + 2v2 = 0

Factor a trinomial.
(1 + -2v)(8 + -1v) = 0


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

Simplifying
1 + -2v = 0

Solving
1 + -2v = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2v = 0 + -1
-2v = 0 + -1

Combine like terms: 0 + -1 = -1
-2v = -1

Divide each side by '-2'.
v = 0.5

Simplifying
v = 0.5

Subproblem 2
Set the factor '(8 + -1v)' equal to zero and attempt to solve:

Simplifying
8 + -1v = 0

Solving
8 + -1v = 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 + -1v = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1v = 0 + -8
-1v = 0 + -8

Combine like terms: 0 + -8 = -8
-1v = -8

Divide each side by '-1'.
v = 8

Simplifying
v = 8
Solution
v = {0.5, 8}

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