Find the Roots (Zeros) (x-4)(-5x+1)=0

$(x - 4) (- 5 x + 1) = 0$

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 4 = 0$

$- 5 x + 1 = 0$

Step 2

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Step 3

Set $- 5 x + 1$ equal to $0$ and solve for $x$ .

Set $- 5 x + 1$ equal to $0$ .

$- 5 x + 1 = 0$

Solve $- 5 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$- 5 x = - 1$

Divide each term in $- 5 x = - 1$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 1$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 1}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 1}{- 5}$

Divide $x$ by $1$ .

$x = \frac{- 1}{- 5}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{1}{5}$

Step 4

The final solution is all the values that make $(x - 4) (- 5 x + 1) = 0$ true.

$x = 4, \frac{1}{5}$

Step 5