6x^2+54xy+48y^2=0

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Solution for 6x^2+54xy+48y^2=0 equation: 


Simplifying
6x2 + 54xy + 48y2 = 0

Reorder the terms:
54xy + 6x2 + 48y2 = 0

Solving
54xy + 6x2 + 48y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(9xy + x2 + 8y2) = 0

Factor a trinomial.
6((x + y)(x + 8y)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

Add '-1y' to each side of the equation.
x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
x + 0 = 0 + -1y
x = 0 + -1y
Remove the zero:
x = -1y

Simplifying
x = -1y

Subproblem 2
Set the factor '(x + 8y)' equal to zero and attempt to solve:

Simplifying
x + 8y = 0

Solving
x + 8y = 0

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

Add '-8y' to each side of the equation.
x + 8y + -8y = 0 + -8y

Combine like terms: 8y + -8y = 0
x + 0 = 0 + -8y
x = 0 + -8y
Remove the zero:
x = -8y

Simplifying
x = -8y
Solution
x = {-1y, -8y}

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