Question

(х-3)(х-4)=(х+5)(х+6)

Answer 1

Х² - 4х - 3х + 12 = х² + 6х + 5х + 30
6х + 5х + 4х + 3х = 12 - 30
18х = -18
х = -1

Answer 2

To solve the given equation, you can start by expanding both sides and then simplifying the expression. Let's proceed step by step:

1. Expand both sides of the equation: (х - 3)(х - 4) = (х + 5)(х + 6)

2. Use the FOIL method (First, Outer, Inner, Last) to perform the multiplication on both sides: х^2 - 4х - 3х + 12 = х^2 + 6х + 5х + 30

3. Simplify the equation: х^2 - 7х + 12 = х^2 + 11х + 30

Now, we have a quadratic equation. To solve for x, let's move all the terms to one side of the equation:

4. Subtract х^2 and 11х from both sides: х^2 - х^2 - 7х - 11х + 12 - 30 = 0

5. Combine like terms: -18х - 18 = 0

6. Move the constant term to the other side: -18х = 18

7. Finally, solve for x: х = 18 / -18

х = -1

So, the solution to the equation is x = -1. You can verify this by substituting -1 back into the original equation to see if both sides are equal.