3x(2x+y)=0

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Solution for 3x(2x+y)=0 equation: 


Simplifying
3x(2x + y) = 0
(2x * 3x + y * 3x) = 0

Reorder the terms:
(3xy + 6x2) = 0
(3xy + 6x2) = 0

Solving
3xy + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(y + 2x) = 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 '(y + 2x)' equal to zero and attempt to solve:

Simplifying
y + 2x = 0

Reorder the terms:
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y
Solution
x = {0, -0.5y}

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