To solve the equation 7(x-1) + 2x(1-x) = 0, we can start by simplifying the expression on the left side:

7(x-1) + 2x(1-x) = 0
7x - 7 + 2x - 2x^2 = 0
7x + 2x - 7 - 2x^2 = 0
9x - 7 - 2x^2 = 0

Next, we can rearrange the equation to form a quadratic equation:

2x^2 - 9x + 7 = 0

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, factoring is the most efficient method:

(2x - 7)(x - 1) = 0

Setting each factor equal to zero, we have:

2x - 7 = 0 or x - 1 = 0

Solving each equation separately:

2x - 7 = 0
2x = 7
x = 7/2

x - 1 = 0
x = 1

Therefore, the solutions to the equation 7(x-1) + 2x(1-x) = 0 are x = 7/2 and x = 1.