# How do you solve (4z + 2) ( 1- z ) = 0?

Mar 20, 2018

See a solution process below:

#### Explanation:

To solve this and find the roots of the equation equate each term on the left to $0$ and solve for $z$:

Solution 1:

$4 z + 2 = 0$

$4 z + 2 - \textcolor{red}{2} = 0 - \textcolor{red}{2}$

$4 z + 0 = - 2$

$4 z = - 2$

$\frac{4 z}{\textcolor{red}{4}} = - \frac{2}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} z}{\cancel{\textcolor{red}{4}}} = - \frac{1}{2}$

$z = - \frac{1}{2}$

Solution 2:

$1 - z = 0$

$1 - z + \textcolor{red}{z} = 0 + \textcolor{red}{z}$

$1 - 0 = z$

$1 = z$

$z = 1$

The Solution Set Is: $z = \left\{- \frac{1}{2} , 1\right\}$