(х-3)(х-4)=(х+5)(х+6)

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To find the solution to this equation, we first need to expand both sides:

(х-3)(х-4) = х^2 - 4х - 3х + 12 = х^2 - 7х + 12
(х+5)(х+6) = х^2 + 6х + 5х + 30 = х^2 + 11х + 30

Now we set the two expanded expressions equal to each other and solve for х:
х^2 - 7х + 12 = х^2 + 11х + 30
Subtracting х^2 from both sides, we get:
-7х + 12 = 11х + 30
Subtracting 11х from both sides, we get:
-18х + 12 = 30
Subtracting 12 from both sides, we get:
-18х = 18
Dividing by -18, we get:
х = -1

Therefore, the solution to the equation (х-3)(х-4) = (х+5)(х+6) is х = -1.