3x(2x-6y-x+7z)=0

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Solution for 3x(2x-6y-x+7z)=0 equation: 


Simplifying
3x(2x + -6y + -1x + 7z) = 0

Reorder the terms:
3x(2x + -1x + -6y + 7z) = 0

Combine like terms: 2x + -1x = 1x
3x(1x + -6y + 7z) = 0
(1x * 3x + -6y * 3x + 7z * 3x) = 0

Reorder the terms:
(-18xy + 21xz + 3x2) = 0
(-18xy + 21xz + 3x2) = 0

Solving
-18xy + 21xz + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-6y + 7z + x) = 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 '(-6y + 7z + x)' equal to zero and attempt to solve:

Simplifying
-6y + 7z + x = 0

Reorder the terms:
x + -6y + 7z = 0

Solving
x + -6y + 7z = 0

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

Add '6y' to each side of the equation.
x + -6y + 6y + 7z = 0 + 6y

Combine like terms: -6y + 6y = 0
x + 0 + 7z = 0 + 6y
x + 7z = 0 + 6y
Remove the zero:
x + 7z = 6y

Add '-7z' to each side of the equation.
x + 7z + -7z = 6y + -7z

Combine like terms: 7z + -7z = 0
x + 0 = 6y + -7z
x = 6y + -7z

Simplifying
x = 6y + -7z
Solution
x = {0, 6y + -7z}

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