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

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Solution for (2z+y)(3z+y)= 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}

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