24x^3(y+6)+48x^2(y+6)-16x(y+6)=

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Solution for 24x^3(y+6)+48x^2(y+6)-16x(y+6)= equation: 


Simplifying
24x3(y + 6) + 48x2(y + 6) + -16x(y + 6) = 0

Reorder the terms:
24x3(6 + y) + 48x2(y + 6) + -16x(y + 6) = 0
(6 * 24x3 + y * 24x3) + 48x2(y + 6) + -16x(y + 6) = 0
(144x3 + 24x3y) + 48x2(y + 6) + -16x(y + 6) = 0

Reorder the terms:
144x3 + 24x3y + 48x2(6 + y) + -16x(y + 6) = 0
144x3 + 24x3y + (6 * 48x2 + y * 48x2) + -16x(y + 6) = 0
144x3 + 24x3y + (288x2 + 48x2y) + -16x(y + 6) = 0

Reorder the terms:
144x3 + 24x3y + 288x2 + 48x2y + -16x(6 + y) = 0
144x3 + 24x3y + 288x2 + 48x2y + (6 * -16x + y * -16x) = 0
144x3 + 24x3y + 288x2 + 48x2y + (-96x + -16xy) = 0

Reorder the terms:
-96x + -16xy + 288x2 + 48x2y + 144x3 + 24x3y = 0

Solving
-96x + -16xy + 288x2 + 48x2y + 144x3 + 24x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x'.
8x(-12 + -2y + 36x + 6xy + 18x2 + 3x2y) = 0

Ignore the factor 8.

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 '(-12 + -2y + 36x + 6xy + 18x2 + 3x2y)' equal to zero and attempt to solve:

Simplifying
-12 + -2y + 36x + 6xy + 18x2 + 3x2y = 0

Reorder the terms:
-12 + 36x + 6xy + 18x2 + 3x2y + -2y = 0

Solving
-12 + 36x + 6xy + 18x2 + 3x2y + -2y = 0

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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