(x-2)(x-4)(x-6)=(x-4)(x-5)(x-6)

2 min read Jun 17, 2024

Solving the Equation (x-2)(x-4)(x-6) = (x-4)(x-5)(x-6)

This equation presents a straightforward algebraic problem that can be solved by applying basic algebraic manipulations. Let's break down the solution step-by-step:

Step 1: Simplifying the Equation

First, we can notice that both sides of the equation share the factors (x-4) and (x-6). Therefore, we can divide both sides by these factors to simplify the equation:

(x-2)(x-4)(x-6) / [(x-4)(x-6)] = (x-4)(x-5)(x-6) / [(x-4)(x-6)]

This simplifies to:

x-2 = x-5

Step 2: Solving for x

Now, we have a simple linear equation. To solve for x, we can subtract x from both sides:

x - 2 - x = x - 5 - x

This simplifies to:

-2 = -5

Step 3: Analyzing the Result

The result, -2 = -5, is a contradiction. This indicates that the original equation has no solution. In other words, there is no value of x that can make the equation true.

Conclusion

The equation (x-2)(x-4)(x-6) = (x-4)(x-5)(x-6) has no solution due to the inherent contradiction in the simplified equation.