0=-100x^5+465x^4-540x^3

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Solution for 0=-100x^5+465x^4-540x^3 equation: 


Simplifying
0 = -100x5 + 465x4 + -540x3

Reorder the terms:
0 = -540x3 + 465x4 + -100x5

Solving
0 = -540x3 + 465x4 + -100x5

Solving for variable 'x'.
Remove the zero:
540x3 + -465x4 + 100x5 = -540x3 + 465x4 + -100x5 + 540x3 + -465x4 + 100x5

Reorder the terms:
540x3 + -465x4 + 100x5 = -540x3 + 540x3 + 465x4 + -465x4 + -100x5 + 100x5

Combine like terms: -540x3 + 540x3 = 0
540x3 + -465x4 + 100x5 = 0 + 465x4 + -465x4 + -100x5 + 100x5
540x3 + -465x4 + 100x5 = 465x4 + -465x4 + -100x5 + 100x5

Combine like terms: 465x4 + -465x4 = 0
540x3 + -465x4 + 100x5 = 0 + -100x5 + 100x5
540x3 + -465x4 + 100x5 = -100x5 + 100x5

Combine like terms: -100x5 + 100x5 = 0
540x3 + -465x4 + 100x5 = 0

Factor out the Greatest Common Factor (GCF), '5x3'.
5x3(108 + -93x + 20x2) = 0

Factor a trinomial.
5x3((9 + -4x)(12 + -5x)) = 0

Ignore the factor 5.

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 '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25

Subproblem 3
Set the factor '(12 + -5x)' equal to zero and attempt to solve:

Simplifying
12 + -5x = 0

Solving
12 + -5x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -5x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -5x = 0 + -12
-5x = 0 + -12

Combine like terms: 0 + -12 = -12
-5x = -12

Divide each side by '-5'.
x = 2.4

Simplifying
x = 2.4
Solution
x = {2.25, 2.4}

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