(5y-2z)(8y-z)=0

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Solution for (5y-2z)(8y-z)=0 equation: 


Simplifying
(5y + -2z)(8y + -1z) = 0

Multiply (5y + -2z) * (8y + -1z)
(5y * (8y + -1z) + -2z * (8y + -1z)) = 0
((8y * 5y + -1z * 5y) + -2z * (8y + -1z)) = 0

Reorder the terms:
((-5yz + 40y2) + -2z * (8y + -1z)) = 0
((-5yz + 40y2) + -2z * (8y + -1z)) = 0
(-5yz + 40y2 + (8y * -2z + -1z * -2z)) = 0
(-5yz + 40y2 + (-16yz + 2z2)) = 0

Reorder the terms:
(-5yz + -16yz + 40y2 + 2z2) = 0

Combine like terms: -5yz + -16yz = -21yz
(-21yz + 40y2 + 2z2) = 0

Solving
-21yz + 40y2 + 2z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5y + -2z)(8y + -1z) = 0


Subproblem 1
Set the factor '(5y + -2z)' equal to zero and attempt to solve:

Simplifying
5y + -2z = 0

Solving
5y + -2z = 0

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

Add '2z' to each side of the equation.
5y + -2z + 2z = 0 + 2z

Combine like terms: -2z + 2z = 0
5y + 0 = 0 + 2z
5y = 0 + 2z
Remove the zero:
5y = 2z

Divide each side by '5'.
y = 0.4z

Simplifying
y = 0.4z

Subproblem 2
Set the factor '(8y + -1z)' equal to zero and attempt to solve:

Simplifying
8y + -1z = 0

Solving
8y + -1z = 0

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

Add 'z' to each side of the equation.
8y + -1z + z = 0 + z

Combine like terms: -1z + z = 0
8y + 0 = 0 + z
8y = 0 + z
Remove the zero:
8y = z

Divide each side by '8'.
y = 0.125z

Simplifying
y = 0.125z
Solution
y = {0.4z, 0.125z}

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