(2z+y)(3z+y)=0

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

Simplifying
(2z + y)(3z + y) = 0

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

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

Multiply (y + 2z) * (y + 3z)
(y(y + 3z) + 2z * (y + 3z)) = 0
((y * y + 3z * y) + 2z * (y + 3z)) = 0

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

Reorder the terms:
(3yz + 2yz + y2 + 6z2) = 0

Combine like terms: 3yz + 2yz = 5yz
(5yz + y2 + 6z2) = 0

Solving
5yz + y2 + 6z2 = 0

Solving for variable 'y'.

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

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

Simplifying
y + 2z = 0

Solving
y + 2z = 0

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

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

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

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

Simplifying
y + 3z = 0

Solving
y + 3z = 0

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

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

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

Simplifying
y = -3z
Solution
y = {-2z, -3z}