Solve (x+1)(x+3)-x=x²: Expanding Brackets and Simplifying

Let's solve the equation, first we'll simplify the algebraic expressions using the extended distribution law:

$(a+b)(c+d)=ac+ad+bc+bd$We will therefore apply the mentioned law and open the parentheses in the expression in the equation:

$(x+1)(x+3)-x=x^2 \\ x^2+3x+x+3 -x=x^2 \\$We'll continue and combine like terms, by moving terms, then - we can notice that the squared term cancels out and therefore it's a first-degree equation, which we'll solve by isolating the variable term on one side and dividing both sides of the equation by its coefficient:

$x^2+3x+x+3 -x=x^2\\ 3x=-3\hspace{8pt}\text{/}:3\\ \boxed{x=-1}$Therefore, the correct answer is answer A.