3x(X^2+3xy+8y^2)=0

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Solution for 3x(X^2+3xy+8y^2)=0 equation: 


Simplifying
3x(X2 + 3xy + 8y2) = 0
(X2 * 3x + 3xy * 3x + 8y2 * 3x) = 0

Reorder the terms:
(3xX2 + 24xy2 + 9x2y) = 0
(3xX2 + 24xy2 + 9x2y) = 0

Solving
3xX2 + 24xy2 + 9x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(X2 + 8y2 + 3xy) = 0

Ignore the factor 3.

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 '(X2 + 8y2 + 3xy)' equal to zero and attempt to solve:

Simplifying
X2 + 8y2 + 3xy = 0

Reorder the terms:
X2 + 3xy + 8y2 = 0

Solving
X2 + 3xy + 8y2 = 0

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

Add '-1X2' to each side of the equation.
X2 + 3xy + -1X2 + 8y2 = 0 + -1X2

Reorder the terms:
X2 + -1X2 + 3xy + 8y2 = 0 + -1X2

Combine like terms: X2 + -1X2 = 0
0 + 3xy + 8y2 = 0 + -1X2
3xy + 8y2 = 0 + -1X2
Remove the zero:
3xy + 8y2 = -1X2

Add '-8y2' to each side of the equation.
3xy + 8y2 + -8y2 = -1X2 + -8y2

Combine like terms: 8y2 + -8y2 = 0
3xy + 0 = -1X2 + -8y2
3xy = -1X2 + -8y2

Divide each side by '3y'.
x = -0.3333333333y-1X2 + -2.666666667y

Simplifying
x = -0.3333333333y-1X2 + -2.666666667y
Solution
x = {0, -0.3333333333y-1X2 + -2.666666667y}

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