(x+2)(x-3)=(x-5)(x-6)

Jasonbradley

3 min read Jun 16, 2024

Solving the Equation (x+2)(x-3) = (x-5)(x-6)

This article will guide you through the steps of solving the equation (x+2)(x-3) = (x-5)(x-6).

Expanding the Equation

First, we need to expand both sides of the equation by multiplying the factors:

Left side: (x+2)(x-3) = x² - x - 6
Right side: (x-5)(x-6) = x² - 11x + 30

Now our equation looks like this: x² - x - 6 = x² - 11x + 30

Simplifying the Equation

Next, let's simplify the equation by combining like terms. We can subtract x² from both sides, which cancels out the x² terms:

-x - 6 = -11x + 30

Now let's isolate the x terms by adding 11x to both sides:

10x - 6 = 30

Finally, add 6 to both sides to isolate the x term:

10x = 36

Solving for x

To solve for x, we divide both sides by 10:

x = 36/10

Simplifying the fraction, we get:

x = 18/5

Checking the Solution

To ensure our solution is correct, we can plug x = 18/5 back into the original equation:

(18/5 + 2)(18/5 - 3) = (18/5 - 5)(18/5 - 6)

Simplifying both sides:

(28/5)(3/5) = (-7/5)(-12/5)
84/25 = 84/25

Since both sides of the equation are equal, we can confirm that x = 18/5 is the correct solution.

Conclusion

By expanding, simplifying, and solving the equation, we have found that the solution for (x+2)(x-3) = (x-5)(x-6) is x = 18/5. Remember to always check your solution by plugging it back into the original equation to ensure its validity.