Find roots of polynomial $$ p(x) = 1-\frac{3}{4}z+\frac{1}{8}z $$

The root of polynomial $ p(z) $ is:

$$ \begin{aligned}z &= \frac{ 8 }{ 5 } \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 8 } $.

$$ \begin{aligned} 1-\frac{3}{4}z+\frac{1}{8}z & = 0 ~~~ / \cdot \color{blue}{ 8 } \\[1 em] 8-6z+z & = 0 \end{aligned} $$

Step 2:

Combine like terms:

$$ 8 \color{blue}{-6z} + \color{blue}{z} = \color{blue}{-5z} +8 $$

Step 3:

$$ \begin{aligned} -5z+8 & = 0 \\[1 em] -5 \cdot z & = -8 \\[1 em] z & = - \frac{ 8 }{ -5 } \\[1 em] z & = \frac{ 8 }{ 5 } \end{aligned} $$

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