(4z+2)(4+z)=0 (If there is more than one solution , separate them with commas.) z= square

To solve the equation $(4z+2)(4+z)=0$, we need to find the values of $z$ that make the equation true.<br /><br />The equation is a product of two factors: $(4z+2)$ and $(4+z)$. For the product to be equal to zero, at least one of the factors must be equal to zero.<br /><br />Let's consider the first factor, $(4z+2)$. To find the value of $z$ that makes this factor equal to zero, we can set it equal to zero and solve for $z$:<br /><br />$4z + 2 = 0$<br /><br />Subtracting 2 from both sides:<br /><br />$4z = -2$<br /><br />Dividing both sides by 4:<br /><br />$z = -\frac{1}{2}$<br /><br />Now let's consider the second factor, $(4+z)$. To find the value of $z$ that makes this factor equal to zero, we can set it equal to zero and solve for $z$:<br /><br />$4 + z = 0$<br /><br />Subtracting 4 from both sides:<br /><br />$z = -4$<br /><br />Therefore, the solutions to the equation $(4z+2)(4+z)=0$ are $z = -\frac{1}{2}$ and $z = -4$.