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

2 min read Jun 17, 2024

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

This equation looks complex, but we can solve it using simple algebraic manipulation. Let's break down the steps:

1. Simplifying the Equation

Notice that both sides of the equation share the factors (x-5) and (x-6). We can divide both sides by these factors to simplify:

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

This leaves us with:

x - 4 = x - 2

2. Isolating x

To solve for x, we need to isolate it on one side of the equation. Subtract x from both sides:

x - 4 - x = x - 2 - x

This simplifies to:

-4 = -2

3. The Solution

This final equation is a contradiction. -4 cannot equal -2. Therefore, there is no solution to the original equation.

Key Takeaway

This example highlights an important point: if you encounter an equation that leads to a contradiction, it means there are no values of x that can satisfy the original equation.