How do I solve the equation x^2 + 6 = -5x

This equation is an example of a quadratic equation, which is noticeable by the presence of the x² term on the left hand side. We begin to solve these types of equations by moving all the terms to one side (often referred to as making the equation equal zero). This leaves us with x² + 5x + 6 = 0. Solving quadratics in this form is done by factorising the equation into two separate brackets (which could be expanded to give the equation we started with. Now in order to do this we have to find two numbers which add up to 5 (for the 5x) and times to make 6 (for the +6). This is the same process we use for all quadratics you'll come across in this form. Those number are in this case 3 and 2 (2+3=5 , 2x3=6). We now write the equation out with these numbers in the brackets as follows; (x + 3)(x +2) = 0. In order for this equation to equal 0, either of the brackets must do so, therefore x must equal either -3 or -2 so the solution is x = -2 , -3.