Chapter 8 - Polynomials and Factoring - 8-5 Factoring x2+bx+c - Practice and Problem-Solving Exercises - Page 516: 42

See below

Let us simplify both sides. The left is already simplified. The right simplifies as follows $$(x-6)(x-4) = x^2 -(6+4)x + (-6)(-4)$$ $$ = x^2-10x+24$$ Thus the mathematician probably forgot to account for the fact that two negatives multiplied together make a positive. Let's do it properly, $$x^2-10x-24 = x^2-12x+2x-24 = x(x-12)+2(x-12) = (x+2)(x-12)$$