Solve by Factoring x(x-3)=54

$x (x - 3) = 54$

Step 1

Subtract $54$ from both sides of the equation.

$x (x - 3) - 54 = 0$

Step 2

Simplify each term.

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 54 = 0$

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 3 - 54 = 0$

Move $- 3$ to the left of $x$ .

$x^{2} - 3 x - 54 = 0$

Step 3

Factor $x^{2} - 3 x - 54$ using the AC method.

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 $- 54$ and whose sum is $- 3$ .

$- 9, 6$

Write the factored form using these integers.

$(x - 9) (x + 6) = 0$

Step 4

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

$x - 9 = 0$

$x + 6 = 0$

Step 5

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

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

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

Step 6

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

Step 7

The final solution is all the values that make $(x - 9) (x + 6) = 0$ true.

$x = 9, - 6$

Solve by Factoring x(x-3)=54

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