0=2x^5-6x^4-x^3+3x^2

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Solution for 0=2x^5-6x^4-x^3+3x^2 equation: 


Simplifying
0 = 2x5 + -6x4 + -1x3 + 3x2

Reorder the terms:
0 = 3x2 + -1x3 + -6x4 + 2x5

Solving
0 = 3x2 + -1x3 + -6x4 + 2x5

Solving for variable 'x'.
Remove the zero:
-3x2 + x3 + 6x4 + -2x5 = 3x2 + -1x3 + -6x4 + 2x5 + -3x2 + x3 + 6x4 + -2x5

Reorder the terms:
-3x2 + x3 + 6x4 + -2x5 = 3x2 + -3x2 + -1x3 + x3 + -6x4 + 6x4 + 2x5 + -2x5

Combine like terms: 3x2 + -3x2 = 0
-3x2 + x3 + 6x4 + -2x5 = 0 + -1x3 + x3 + -6x4 + 6x4 + 2x5 + -2x5
-3x2 + x3 + 6x4 + -2x5 = -1x3 + x3 + -6x4 + 6x4 + 2x5 + -2x5

Combine like terms: -1x3 + x3 = 0
-3x2 + x3 + 6x4 + -2x5 = 0 + -6x4 + 6x4 + 2x5 + -2x5
-3x2 + x3 + 6x4 + -2x5 = -6x4 + 6x4 + 2x5 + -2x5

Combine like terms: -6x4 + 6x4 = 0
-3x2 + x3 + 6x4 + -2x5 = 0 + 2x5 + -2x5
-3x2 + x3 + 6x4 + -2x5 = 2x5 + -2x5

Combine like terms: 2x5 + -2x5 = 0
-3x2 + x3 + 6x4 + -2x5 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-3 + x + 6x2 + -2x3) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-3 + x + 6x2 + -2x3)' equal to zero and attempt to solve:

Simplifying
-3 + x + 6x2 + -2x3 = 0

Solving
-3 + x + 6x2 + -2x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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