Trigonometry Examples

$x (x - 20) + 3 (x - 20) = 0$

Step 1

Simplify $x (x - 20) + 3 (x - 20)$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$x \cdot x + x \cdot - 20 + 3 (x - 20) = 0$

Step 1.1.2

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 20 + 3 (x - 20) = 0$

Step 1.1.3

Move $- 20$ to the left of $x$ .

$x^{2} - 20 \cdot x + 3 (x - 20) = 0$

Step 1.1.4

Apply the distributive property.

$x^{2} - 20 x + 3 x + 3 \cdot - 20 = 0$

Step 1.1.5

Multiply $3$ by $- 20$ .

$x^{2} - 20 x + 3 x - 60 = 0$

Step 1.2

Add $- 20 x$ and $3 x$ .

$x^{2} - 17 x - 60 = 0$

Step 2

Factor $x^{2} - 17 x - 60$ using the AC method.

Tap for more steps...

Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 60$ and whose sum is $- 17$ .

$- 20, 3$

Step 2.2

Write the factored form using these integers.

$(x - 20) (x + 3) = 0$

Step 3

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

$x - 20 = 0$

$x + 3 = 0$

Step 4

Set $x - 20$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 4.1

Set $x - 20$ equal to $0$ .

$x - 20 = 0$

Step 4.2

Add $20$ to both sides of the equation.

$x = 20$

Step 5

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

Tap for more steps...

Step 5.1

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

$x + 3 = 0$

Step 5.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 6

The final solution is all the values that make $(x - 20) (x + 3) = 0$ true.

$x = 20, - 3$