Question

Solve the equation. $$(x+12)(x+7)=0$

Short answer

The solutions to the equation are \(x=-12\) and \(x=-7\)

Step-by-step solution

Apply Zero-Product Property

According to the zero-product property, if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each \(x+12\) and \(x+7\) equal to zero.

Solve the First Equation

Having \(x+12=0\), we can solve for \(x\) by subtracting \(12\) from both sides to get \(x=-12\).

Solve the Second Equation

Likewise, for \(x+7=0\), subtracting \(7\) from both sides will yield \(x=-7\).