Pre-Algebra Examples

$3 x (2 x - 3) (3 x + 4) = 0$

Step 1

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

$x = 0$

$2 x - 3 = 0$

$3 x + 4 = 0$

Step 2

Set $x$ equal to $0$ .

$x = 0$

Step 3

Set $2 x - 3$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 3.1

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Step 3.2

Solve $2 x - 3 = 0$ for $x$ .

Tap for more steps...

Step 3.2.1

Add $3$ to both sides of the equation.

$2 x = 3$

Step 3.2.2

Divide each term in $2 x = 3$ by $2$ and simplify.

Tap for more steps...

Step 3.2.2.1

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Step 3.2.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Step 3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 4

Set $3 x + 4$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 4.1

Set $3 x + 4$ equal to $0$ .

$3 x + 4 = 0$

Step 4.2

Solve $3 x + 4 = 0$ for $x$ .

Tap for more steps...

Step 4.2.1

Subtract $4$ from both sides of the equation.

$3 x = - 4$

Step 4.2.2

Divide each term in $3 x = - 4$ by $3$ and simplify.

Tap for more steps...

Step 4.2.2.1

Divide each term in $3 x = - 4$ by $3$ .

$\frac{3 x}{3} = \frac{- 4}{3}$

Step 4.2.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 4}{3}$

Step 4.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{3}$

Step 4.2.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

Step 5

The final solution is all the values that make $3 x (2 x - 3) (3 x + 4) = 0$ true.

$x = 0, \frac{3}{2}, - \frac{4}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 0, \frac{3}{2}, - \frac{4}{3}$

Decimal Form:

$x = 0, 1.5, - 1.\overline{3}$

Mixed Number Form:

$x = 0, 1 \frac{1}{2}, - 1 \frac{1}{3}$