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

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


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

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

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

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

Solving
12xy = 14xz

Solving for variable 'x'.

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

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

Combine like terms: 14xz + -14xz = 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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