(7x + 2)(x – 2) = 4(x – 2)2.

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To solve this equation, first expand both sides:

(7x + 2)(x - 2) = (7x^2 - 14x + 2x - 4) = 7x^2 - 12x - 4

4(x - 2)^2 = 4(x^2 - 4x + 4) = 4x^2 - 16x + 16

Now set the two expanded expressions equal to each other:

7x^2 - 12x - 4 = 4x^2 - 16x + 16

Subtract 4x^2 and 16x from both sides:

3x^2 - 28x - 4 = 0

Now, we have a quadratic equation to solve. We can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 3, b = -28, and c = -4:

x = (28 ± √((-28)^2 - 4(3)(-4))) / 2(3)
x = (28 ± √(784 + 48)) / 6
x = (28 ± √832) / 6
x = (28 ± 28.85) / 6

Therefore, the solutions are:
x = (28 + 28.85) / 6 = 9.81
x = (28 - 28.85) / 6 = -0.14

So the solutions to the equation are x = 9.81 and x = -0.14.