10x^7+32x^6+6x^5=0

Solution for 10x^7+32x^6+6x^5=0 equation:

Simplifying
10x7 + 32x6 + 6x5 = 0

Reorder the terms:
6x5 + 32x6 + 10x7 = 0

Solving
6x5 + 32x6 + 10x7 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x5'.
2x5(3 + 16x + 5x2) = 0

Factor a trinomial.
2x5((3 + x)(1 + 5x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x5' equal to zero and attempt to solve:

Simplifying
x5 = 0

Solving
x5 = 0

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

Simplifying
x5 = 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Subproblem 3
Set the factor '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 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 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {-3, -0.2}