z(14x+16y)=y(12x+16z)

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Solution for z(14x+16y)=y(12x+16z) equation: 


Simplifying
z(14x + 16y) = y(12x + 16z)
(14x * z + 16y * z) = y(12x + 16z)
(14xz + 16yz) = y(12x + 16z)
14xz + 16yz = (12x * y + 16z * y)
14xz + 16yz = (12xy + 16yz)

Add '-16yz' to each side of the equation.
14xz + 16yz + -16yz = 12xy + 16yz + -16yz

Combine like terms: 16yz + -16yz = 0
14xz + 0 = 12xy + 16yz + -16yz
14xz = 12xy + 16yz + -16yz

Combine like terms: 16yz + -16yz = 0
14xz = 12xy + 0
14xz = 12xy

Solving
14xz = 12xy

Solving for variable 'x'.

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

Add '-12xy' to each side of the equation.
-12xy + 14xz = 12xy + -12xy

Combine like terms: 12xy + -12xy = 0
-12xy + 14xz = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-6y + 7z) = 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 '(-6y + 7z)' equal to zero and attempt to solve:

Simplifying
-6y + 7z = 0

Solving
-6y + 7z = 0

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

Add '6y' to each side of the equation.
-6y + 6y + 7z = 0 + 6y

Combine like terms: -6y + 6y = 0
0 + 7z = 0 + 6y
7z = 0 + 6y
Remove the zero:
7z = 6y

Add '-7z' to each side of the equation.
7z + -7z = 6y + -7z

Combine like terms: 7z + -7z = 0
0 = 6y + -7z

Simplifying
0 = 6y + -7z

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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