Question

Solve the equation x^2-2zx+3xy-6zy=0 for x in terms of y and z

Answer 1

x = 2z

x = -3y

Step-by-step explanation:

Given the below quadratic equation;

`x^2-2zx+3xy-6zy=0`

Let's go ahead and factor the above completely as seen below;

`\begin{gathered} x(x-2z)+3y(x-2z)=0 \\ (x-2z)(x+3y)=0 \end{gathered}`

We'll now apply the Zero-product property which states that if the product of two numbers is equal to zero, it means that at least one of the numbers is equal to zero.

Applying the Zero-product rule, we'll have;

`\begin{gathered} x-2z=0 \\ x=2z \\ Or \\ x+3y=0 \\ x=-3y \end{gathered}`