(9x^3+x^2-5x)(6xy)=

Solution for (9x^3+x^2-5x)(6xy)= equation:

Simplifying
(9x3 + x2 + -5x)(6xy) = 0

Reorder the terms:
(-5x + x2 + 9x3)(6xy) = 0

Remove parenthesis around (6xy)
(-5x + x2 + 9x3) * 6xy = 0

Reorder the terms for easier multiplication:
6xy(-5x + x2 + 9x3) = 0
(-5x * 6xy + x2 * 6xy + 9x3 * 6xy) = 0
(-30x2y + 6x3y + 54x4y) = 0

Solving
-30x2y + 6x3y + 54x4y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x2y'.
6x2y(-5 + x + 9x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'x2y' equal to zero and attempt to solve:

Simplifying
x2y = 0

Solving
x2y = 0

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

Simplifying
x2y = 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 '(-5 + x + 9x2)' equal to zero and attempt to solve:

Simplifying
-5 + x + 9x2 = 0

Solving
-5 + x + 9x2 = 0

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

Divide each side by '9'.
-0.5555555556 + 0.1111111111x + x2 = 0

Move the constant term to the right:

Add '0.5555555556' to each side of the equation.
-0.5555555556 + 0.1111111111x + 0.5555555556 + x2 = 0 + 0.5555555556

Reorder the terms:
-0.5555555556 + 0.5555555556 + 0.1111111111x + x2 = 0 + 0.5555555556

Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000
0.0000000000 + 0.1111111111x + x2 = 0 + 0.5555555556
0.1111111111x + x2 = 0 + 0.5555555556

Combine like terms: 0 + 0.5555555556 = 0.5555555556
0.1111111111x + x2 = 0.5555555556

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1111111111x + 0.25 + x2 = 0.5555555556 + 0.25

Reorder the terms:
0.25 + 0.1111111111x + x2 = 0.5555555556 + 0.25

Combine like terms: 0.5555555556 + 0.25 = 0.8055555556
0.25 + 0.1111111111x + x2 = 0.8055555556

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.8055555556

Calculate the square root of the right side: 0.897527468

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.897527468 and -0.897527468.

Subproblem 1
x + 0.5 = 0.897527468

Simplifying
x + 0.5 = 0.897527468

Reorder the terms:
0.5 + x = 0.897527468

Solving
0.5 + x = 0.897527468

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.897527468 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.897527468 + -0.5
x = 0.897527468 + -0.5

Combine like terms: 0.897527468 + -0.5 = 0.397527468
x = 0.397527468

Simplifying
x = 0.397527468

Subproblem 2
x + 0.5 = -0.897527468

Simplifying
x + 0.5 = -0.897527468

Reorder the terms:
0.5 + x = -0.897527468

Solving
0.5 + x = -0.897527468

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.897527468 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.897527468 + -0.5
x = -0.897527468 + -0.5

Combine like terms: -0.897527468 + -0.5 = -1.397527468
x = -1.397527468

Simplifying
x = -1.397527468

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.397527468, -1.397527468}
Solution
x = {0.397527468, -1.397527468}