-10x^7-25x^6+20x^5(6x+3)=0

Solution for -10x^7-25x^6+20x^5(6x+3)=0 equation:

Simplifying
-10x7 + -25x6 + 20x5(6x + 3) = 0

Reorder the terms:
-10x7 + -25x6 + 20x5(3 + 6x) = 0
-10x7 + -25x6 + (3 * 20x5 + 6x * 20x5) = 0
-10x7 + -25x6 + (60x5 + 120x6) = 0

Reorder the terms:
60x5 + -25x6 + 120x6 + -10x7 = 0

Combine like terms: -25x6 + 120x6 = 95x6
60x5 + 95x6 + -10x7 = 0

Solving
60x5 + 95x6 + -10x7 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x5'.
5x5(12 + 19x + -2x2) = 0

Ignore the factor 5.
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 '(12 + 19x + -2x2)' equal to zero and attempt to solve:

Simplifying
12 + 19x + -2x2 = 0

Solving
12 + 19x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-6 + -9.5x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -9.5x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -9.5x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -9.5x + x2 = 0 + 6
-9.5x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-9.5x + x2 = 6

The x term is -9.5x.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5x + 22.5625 + x2 = 6 + 22.5625

Reorder the terms:
22.5625 + -9.5x + x2 = 6 + 22.5625

Combine like terms: 6 + 22.5625 = 28.5625
22.5625 + -9.5x + x2 = 28.5625

Factor a perfect square on the left side:
(x + -4.75)(x + -4.75) = 28.5625

Calculate the square root of the right side: 5.344389582

Break this problem into two subproblems by setting 
(x + -4.75) equal to 5.344389582 and -5.344389582.

Subproblem 1
x + -4.75 = 5.344389582

Simplifying
x + -4.75 = 5.344389582

Reorder the terms:
-4.75 + x = 5.344389582

Solving
-4.75 + x = 5.344389582

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = 5.344389582 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = 5.344389582 + 4.75
x = 5.344389582 + 4.75

Combine like terms: 5.344389582 + 4.75 = 10.094389582
x = 10.094389582

Simplifying
x = 10.094389582

Subproblem 2
x + -4.75 = -5.344389582

Simplifying
x + -4.75 = -5.344389582

Reorder the terms:
-4.75 + x = -5.344389582

Solving
-4.75 + x = -5.344389582

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = -5.344389582 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = -5.344389582 + 4.75
x = -5.344389582 + 4.75

Combine like terms: -5.344389582 + 4.75 = -0.594389582
x = -0.594389582

Simplifying
x = -0.594389582

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.094389582, -0.594389582}
Solution
x = {10.094389582, -0.594389582}