5x^7+25x^4+65x=0

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Solution for 5x^7+25x^4+65x=0 equation: 


Simplifying
5x7 + 25x4 + 65x = 0

Reorder the terms:
65x + 25x4 + 5x7 = 0

Solving
65x + 25x4 + 5x7 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(13 + 5x3 + x6) = 0

Ignore the factor 5.

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(13 + 5x3 + x6)' equal to zero and attempt to solve:

Simplifying
13 + 5x3 + x6 = 0

Solving
13 + 5x3 + x6 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 5x3 + -13 + x6 = 0 + -13

Reorder the terms:
13 + -13 + 5x3 + x6 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 5x3 + x6 = 0 + -13
5x3 + x6 = 0 + -13

Combine like terms: 0 + -13 = -13
5x3 + x6 = -13

The x term is 5x3.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x3 + 6.25 + x6 = -13 + 6.25

Reorder the terms:
6.25 + 5x3 + x6 = -13 + 6.25

Combine like terms: -13 + 6.25 = -6.75
6.25 + 5x3 + x6 = -6.75

Factor a perfect square on the left side:
(x3 + 2.5)(x3 + 2.5) = -6.75

Can't calculate square root of the right side.

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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