Solve for x 3x(x-5)(5x+8)=0

$3 x (x - 5) (5 x + 8) = 0$

Step 1

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

$x = 0$

$x - 5 = 0$

$5 x + 8 = 0$

Step 2

Set $x$ equal to $0$ .

$x = 0$

Step 3

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

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

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Step 4

Set $5 x + 8$ equal to $0$ and solve for $x$ .

Set $5 x + 8$ equal to $0$ .

$5 x + 8 = 0$

Solve $5 x + 8 = 0$ for $x$ .

Subtract $8$ from both sides of the equation.

$5 x = - 8$

Divide each term in $5 x = - 8$ by $5$ and simplify.

Divide each term in $5 x = - 8$ by $5$ .

$\frac{5 x}{5} = \frac{- 8}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 8}{5}$

Divide $x$ by $1$ .

$x = \frac{- 8}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{8}{5}$

Step 5

The final solution is all the values that make $3 x (x - 5) (5 x + 8) = 0$ true.

$x = 0, 5, - \frac{8}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 0, 5, - \frac{8}{5}$

Decimal Form:

$x = 0, 5, - 1.6$

Mixed Number Form:

$x = 0, 5, - 1 \frac{3}{5}$