(х-4)(4х+6)=(х-5)(х-5)

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To solve this equation, let's first expand both sides:

(х-4)(4х+6) = x(4x) + x(6) - 4(4x) - 4(6)
= 4x^2 + 6x - 16x - 24
= 4x^2 - 10x - 24

(x-5)(x-5) = x(x) - x(5) - 5(x) + 5(5)
= x^2 - 5x - 5x + 25
= x^2 - 10x + 25

Now, we can set the two sides equal to each other:

4x^2 - 10x - 24 = x^2 - 10x + 25

Subtract x^2 and add 10x to both sides:

3x^2 - 24 = 25

Now, add 24 to both sides:

3x^2 = 49

Finally, divide by 3 to solve for x:

x^2 = 49/3

x = ±√(49/3) = ±√(49)/√3 = ±7/√3

So, the solution to the equation (х-4)(4х+6)=(х-5)(х-5) is x = ±7/√3.