2x^2+4xy-6xz=0

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Solution for 2x^2+4xy-6xz=0 equation: 


Simplifying
2x2 + 4xy + -6xz = 0

Reorder the terms:
4xy + -6xz + 2x2 = 0

Solving
4xy + -6xz + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(2y + -3z + x) = 0

Ignore the factor 2.

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 '(2y + -3z + x)' equal to zero and attempt to solve:

Simplifying
2y + -3z + x = 0

Reorder the terms:
x + 2y + -3z = 0

Solving
x + 2y + -3z = 0

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

Add '-2y' to each side of the equation.
x + 2y + -2y + -3z = 0 + -2y

Combine like terms: 2y + -2y = 0
x + 0 + -3z = 0 + -2y
x + -3z = 0 + -2y
Remove the zero:
x + -3z = -2y

Add '3z' to each side of the equation.
x + -3z + 3z = -2y + 3z

Combine like terms: -3z + 3z = 0
x + 0 = -2y + 3z
x = -2y + 3z

Simplifying
x = -2y + 3z
Solution
x = {0, -2y + 3z}

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