0=3x^5+5x^4-2x^3

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Solution for 0=3x^5+5x^4-2x^3 equation: 


Simplifying
0 = 3x5 + 5x4 + -2x3

Reorder the terms:
0 = -2x3 + 5x4 + 3x5

Solving
0 = -2x3 + 5x4 + 3x5

Solving for variable 'x'.
Remove the zero:
2x3 + -5x4 + -3x5 = -2x3 + 5x4 + 3x5 + 2x3 + -5x4 + -3x5

Reorder the terms:
2x3 + -5x4 + -3x5 = -2x3 + 2x3 + 5x4 + -5x4 + 3x5 + -3x5

Combine like terms: -2x3 + 2x3 = 0
2x3 + -5x4 + -3x5 = 0 + 5x4 + -5x4 + 3x5 + -3x5
2x3 + -5x4 + -3x5 = 5x4 + -5x4 + 3x5 + -3x5

Combine like terms: 5x4 + -5x4 = 0
2x3 + -5x4 + -3x5 = 0 + 3x5 + -3x5
2x3 + -5x4 + -3x5 = 3x5 + -3x5

Combine like terms: 3x5 + -3x5 = 0
2x3 + -5x4 + -3x5 = 0

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(2 + -5x + -3x2) = 0

Factor a trinomial.
x3((1 + -3x)(2 + x)) = 0


Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 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 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {0.3333333333, -2}

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