Question

Solve the equation. $$(x+5)(x+6)=0$$

Short answer

The solution to the equation is \(x=-5, -6\)

Step-by-step solution

Apply the Zero Product Property

Since we have \((x+5)(x+6)=0\), we apply the Zero product property. This property states that for real numbers 'a' and 'b'. If \(ab=0\) then \(a=0\) or \(b=0\). So to solve this equation, set each factor equal to zero.

Solve for x in the first factor

In the first factor, \(x+5=0\), subtract 5 from both sides to isolate x. This results in \(x=-5\). So, the first solution is \(x=-5\).

Solve for x in the second factor

In the second factor, \(x+6=0\), subtract 6 from both sides to isolate x. This gives the solution \(x=-6\). Thus the second solution is \(x=-6\).