Calling the middle one x, the three consecutive odd integers would be x-2, x and x+2.

'Four times the sum of three consecutive odd integers' is 4(x-2+x+x+2), which is 4(3x), which is 12x.

'three times the product of the larger two numbers' is 3x(x+2), which is 3x²+6x.

We are told that 12x is 765 less than 3x²+6x, so the equation is 12x + 765 = 3x² + 6x.

Put into standard quadratic form: 3x² - 6x - 765 = 0

Simplify: x² - 2x - 255 = 0

Factorise: (x-17)(x+15) = 0

Solve: x = 17 or -15.

This means that the three integers are either {15, 17, 19} or {-17, -15, -13}.