y(8x+8z)=z(10x+8y)

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Solution for y(8x+8z)=z(10x+8y) equation: 


Simplifying
y(8x + 8z) = z(10x + 8y)
(8x * y + 8z * y) = z(10x + 8y)
(8xy + 8yz) = z(10x + 8y)
8xy + 8yz = (10x * z + 8y * z)
8xy + 8yz = (10xz + 8yz)

Add '-8yz' to each side of the equation.
8xy + 8yz + -8yz = 10xz + 8yz + -8yz

Combine like terms: 8yz + -8yz = 0
8xy + 0 = 10xz + 8yz + -8yz
8xy = 10xz + 8yz + -8yz

Combine like terms: 8yz + -8yz = 0
8xy = 10xz + 0
8xy = 10xz

Solving
8xy = 10xz

Solving for variable 'x'.

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

Add '-10xz' to each side of the equation.
8xy + -10xz = 10xz + -10xz

Combine like terms: 10xz + -10xz = 0
8xy + -10xz = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(4y + -5z) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(4y + -5z)' equal to zero and attempt to solve:

Simplifying
4y + -5z = 0

Solving
4y + -5z = 0

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

Add '-4y' to each side of the equation.
4y + -4y + -5z = 0 + -4y

Combine like terms: 4y + -4y = 0
0 + -5z = 0 + -4y
-5z = 0 + -4y
Remove the zero:
-5z = -4y

Add '5z' to each side of the equation.
-5z + 5z = -4y + 5z

Combine like terms: -5z + 5z = 0
0 = -4y + 5z

Simplifying
0 = -4y + 5z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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