Solving the Equation (x+2)(x3) = (x5)(x6)
This article will guide you through the steps of solving the equation (x+2)(x3) = (x5)(x6).
Expanding the Equation
First, we need to expand both sides of the equation by multiplying the factors:
 Left side: (x+2)(x3) = x²  x  6
 Right side: (x5)(x6) = 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)(x3) = (x5)(x6) is x = 18/5. Remember to always check your solution by plugging it back into the original equation to ensure its validity.