Trigonometry Examples

$(x - 1) (x + 2) (3 - x) = 0$

Step 1

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

$x - 1 = 0$

$x + 2 = 0$

$3 - x = 0$

Step 2

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

Tap for more steps...

Step 2.1

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

$x - 1 = 0$

Step 2.2

Add $1$ to both sides of the equation.

$x = 1$

Step 3

Set $x + 2$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 3.1

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Step 3.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 4

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

Tap for more steps...

Step 4.1

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

$3 - x = 0$

Step 4.2

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

Tap for more steps...

Step 4.2.1

Subtract $3$ from both sides of the equation.

$- x = - 3$

Step 4.2.2

Divide each term in $- x = - 3$ by $- 1$ and simplify.

Tap for more steps...

Step 4.2.2.1

Divide each term in $- x = - 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 3}{- 1}$

Step 4.2.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 3}{- 1}$

Step 4.2.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 3}{- 1}$

Step 4.2.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.2.3.1

Divide $- 3$ by $- 1$ .

$x = 3$

Step 5

The final solution is all the values that make $(x - 1) (x + 2) (3 - x) = 0$ true.

$x = 1, - 2, 3$