Expanding the equation, we get:

(-8x + 3y)(5y + x) - (-6x + 4y)(3y - 5x)

= (-8x)(5y) + (-8x)(x) + (3y)(5y) + (3y)(x) - (-6x)(3y) + (-6x)(-5x) + (4y)(3y) - (4y)(-5x)

= -40xy - 8x^2 + 15y^2 + 3xy + 18xy + 30x + 12y^2 + 20xy

= -40xy - 8x^2 + 15y^2 + 3xy + 18xy + 30x + 12y^2 + 20xy

= -8x^2 - 40xy + 3xy + 18xy + 20xy + 30x + 15y^2 + 12y^2

= -8x^2 - 8xy + 6xy + 30x + 27y^2

= -8x^2 - 2xy + 30x + 27y^2

Therefore, the expression simplifies to -8x^2 - 2xy + 30x + 27y^2.