0=12v^5+16v^4-28v^3

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Solution for 0=12v^5+16v^4-28v^3 equation: 


Simplifying
0 = 12v5 + 16v4 + -28v3

Reorder the terms:
0 = -28v3 + 16v4 + 12v5

Solving
0 = -28v3 + 16v4 + 12v5

Solving for variable 'v'.
Remove the zero:
28v3 + -16v4 + -12v5 = -28v3 + 16v4 + 12v5 + 28v3 + -16v4 + -12v5

Reorder the terms:
28v3 + -16v4 + -12v5 = -28v3 + 28v3 + 16v4 + -16v4 + 12v5 + -12v5

Combine like terms: -28v3 + 28v3 = 0
28v3 + -16v4 + -12v5 = 0 + 16v4 + -16v4 + 12v5 + -12v5
28v3 + -16v4 + -12v5 = 16v4 + -16v4 + 12v5 + -12v5

Combine like terms: 16v4 + -16v4 = 0
28v3 + -16v4 + -12v5 = 0 + 12v5 + -12v5
28v3 + -16v4 + -12v5 = 12v5 + -12v5

Combine like terms: 12v5 + -12v5 = 0
28v3 + -16v4 + -12v5 = 0

Factor out the Greatest Common Factor (GCF), '4v3'.
4v3(7 + -4v + -3v2) = 0

Factor a trinomial.
4v3((1 + -1v)(7 + 3v)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'v3' equal to zero and attempt to solve:

Simplifying
v3 = 0

Solving
v3 = 0

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

Simplifying
v3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
1 + -1v = 0

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

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

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

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

Simplifying
v = 1

Subproblem 3
Set the factor '(7 + 3v)' equal to zero and attempt to solve:

Simplifying
7 + 3v = 0

Solving
7 + 3v = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3v = 0 + -7
3v = 0 + -7

Combine like terms: 0 + -7 = -7
3v = -7

Divide each side by '3'.
v = -2.333333333

Simplifying
v = -2.333333333
Solution
v = {1, -2.333333333}

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