(3y-2z)(6y-z)=0

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


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

Multiply (3y + -2z) * (6y + -1z)
(3y * (6y + -1z) + -2z * (6y + -1z)) = 0
((6y * 3y + -1z * 3y) + -2z * (6y + -1z)) = 0

Reorder the terms:
((-3yz + 18y2) + -2z * (6y + -1z)) = 0
((-3yz + 18y2) + -2z * (6y + -1z)) = 0
(-3yz + 18y2 + (6y * -2z + -1z * -2z)) = 0
(-3yz + 18y2 + (-12yz + 2z2)) = 0

Reorder the terms:
(-3yz + -12yz + 18y2 + 2z2) = 0

Combine like terms: -3yz + -12yz = -15yz
(-15yz + 18y2 + 2z2) = 0

Solving
-15yz + 18y2 + 2z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3y + -2z)(6y + -1z) = 0


Subproblem 1
Set the factor '(3y + -2z)' equal to zero and attempt to solve:

Simplifying
3y + -2z = 0

Solving
3y + -2z = 0

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

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

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

Divide each side by '3'.
y = 0.6666666667z

Simplifying
y = 0.6666666667z

Subproblem 2
Set the factor '(6y + -1z)' equal to zero and attempt to solve:

Simplifying
6y + -1z = 0

Solving
6y + -1z = 0

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

Add 'z' to each side of the equation.
6y + -1z + z = 0 + z

Combine like terms: -1z + z = 0
6y + 0 = 0 + z
6y = 0 + z
Remove the zero:
6y = z

Divide each side by '6'.
y = 0.1666666667z

Simplifying
y = 0.1666666667z
Solution
y = {0.6666666667z, 0.1666666667z}

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