Precalculus Examples

${(x - 6)}^{2} (x + 9) < 0$

Step 1

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

${(x - 6)}^{2} = 0$

$x + 9 = 0$

Step 2

Set ${(x - 6)}^{2}$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.1

Set ${(x - 6)}^{2}$ equal to $0$ .

${(x - 6)}^{2} = 0$

Step 2.2

Solve ${(x - 6)}^{2} = 0$ for $x$ .

Tap for more steps...

Step 2.2.1

Set the $x - 6$ equal to $0$ .

$x - 6 = 0$

Step 2.2.2

Add $6$ to both sides of the equation.

$x = 6$

Step 3

Set $x + 9$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 3.1

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Step 3.2

Subtract $9$ from both sides of the equation.

$x = - 9$

Step 4

The final solution is all the values that make ${(x - 6)}^{2} (x + 9) < 0$ true.

$x = 6, - 9$

Step 5

The solution consists of all of the true intervals.

$x < - 9$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < - 9$

Interval Notation:

$(- \infty, - 9)$

Step 7