(6z+4y-2y)(z+5z-2y)=0

Solution for (6z+4y-2y)(z+5z-2y)=0 equation:

Simplifying
(6z + 4y + -2y)(z + 5z + -2y) = 0

Reorder the terms:
(4y + -2y + 6z)(z + 5z + -2y) = 0

Combine like terms: 4y + -2y = 2y
(2y + 6z)(z + 5z + -2y) = 0

Reorder the terms:
(2y + 6z)(-2y + z + 5z) = 0

Combine like terms: z + 5z = 6z
(2y + 6z)(-2y + 6z) = 0

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

Reorder the terms:
((12yz + -4y2) + 6z * (-2y + 6z)) = 0
((12yz + -4y2) + 6z * (-2y + 6z)) = 0
(12yz + -4y2 + (-2y * 6z + 6z * 6z)) = 0
(12yz + -4y2 + (-12yz + 36z2)) = 0

Reorder the terms:
(12yz + -12yz + -4y2 + 36z2) = 0

Combine like terms: 12yz + -12yz = 0
(0 + -4y2 + 36z2) = 0
(-4y2 + 36z2) = 0

Solving
-4y2 + 36z2 = 0

Solving for variable 'y'.

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

Add '-36z2' to each side of the equation.
-4y2 + 36z2 + -36z2 = 0 + -36z2

Combine like terms: 36z2 + -36z2 = 0
-4y2 + 0 = 0 + -36z2
-4y2 = 0 + -36z2
Remove the zero:
-4y2 = -36z2

Divide each side by '-4'.
y2 = 9z2

Simplifying
y2 = 9z2

Take the square root of each side:
y = {-3z, 3z}