(3z+6y)(2z-4y)=

Solution for (3z+6y)(2z-4y)= equation:

Simplifying
(3z + 6y)(2z + -4y) = 0

Reorder the terms:
(6y + 3z)(2z + -4y) = 0

Reorder the terms:
(6y + 3z)(-4y + 2z) = 0

Multiply (6y + 3z) * (-4y + 2z)
(6y * (-4y + 2z) + 3z * (-4y + 2z)) = 0
((-4y * 6y + 2z * 6y) + 3z * (-4y + 2z)) = 0

Reorder the terms:
((12yz + -24y2) + 3z * (-4y + 2z)) = 0
((12yz + -24y2) + 3z * (-4y + 2z)) = 0
(12yz + -24y2 + (-4y * 3z + 2z * 3z)) = 0
(12yz + -24y2 + (-12yz + 6z2)) = 0

Reorder the terms:
(12yz + -12yz + -24y2 + 6z2) = 0

Combine like terms: 12yz + -12yz = 0
(0 + -24y2 + 6z2) = 0
(-24y2 + 6z2) = 0

Solving
-24y2 + 6z2 = 0

Solving for variable 'y'.

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

Add '-6z2' to each side of the equation.
-24y2 + 6z2 + -6z2 = 0 + -6z2

Combine like terms: 6z2 + -6z2 = 0
-24y2 + 0 = 0 + -6z2
-24y2 = 0 + -6z2
Remove the zero:
-24y2 = -6z2

Divide each side by '-24'.
y2 = 0.25z2

Simplifying
y2 = 0.25z2

Take the square root of each side:
y = {-0.5z, 0.5z}