To solve this equation, we first expand both sides:

(x+1)(x+2) = (x)(x) + (x)(2) + (1)(x) + (1)(2)
= x^2 + 2x + x + 2
= x^2 + 3x + 2

(2x-1)(2x-10) = (2x)(2x) + (2x)(-10) + (-1)(2x) + (-1)(-10)
= 4x^2 - 20x - 2x + 10
= 4x^2 - 22x + 10

Setting the two expanded expressions equal to each other, we have:

x^2 + 3x + 2 = 4x^2 - 22x + 10

Rearranging terms, we get:

0 = 4x^2 - 22x + 10 - x^2 - 3x - 2
0 = 3x^2 - 25x + 8

Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula.

Using the quadratic formula, we have:

x = [-(-25) ± √((-25)^2 - 4(3)(8))] / 2(3)
x = [25 ± √(625 - 96)] / 6
x = [25 ± √529] / 6
x = [25 ± 23] / 6

Therefore, the solutions are:

x = (25 + 23) / 6 = 8
x = (25 - 23) / 6 = 2/3

Therefore, the solutions to the equation are x = 8 and x = 2/3.