(x-2)(x-4)(x-6)=(x-2)(x-3)(x-6)

2 min read Jun 17, 2024

Solving the Equation (x-2)(x-4)(x-6) = (x-2)(x-3)(x-6)

This equation presents a unique challenge as it involves a product of three binomials on each side. Let's break down the steps to solve it:

1. Simplify by Canceling Common Factors

Notice that both sides of the equation share the factors (x-2) and (x-6). We can cancel these factors from both sides to simplify the equation:

(x-2)(x-4)(x-6) = (x-2)(x-3)(x-6)

(x-4) = (x-3)

2. Solve for x

Now we have a simple linear equation. To solve for x, we can isolate it on one side:

(x-4) = (x-3)

x - x = -3 + 4

0 = 1

3. Interpreting the Solution

The equation 0 = 1 is a contradiction. This means there is no solution for x that satisfies the original equation.

Conclusion

The equation (x-2)(x-4)(x-6) = (x-2)(x-3)(x-6) has no solution. This is because the simplification process leads to a contradiction, indicating that the original equation is not possible for any value of x.