Solve by Factoring x^3-12x^2+27x=0

$x^{3} - 12 x^{2} + 27 x = 0$

Step 1

Factor $x$ out of $x^{3} - 12 x^{2} + 27 x$ .

Factor $x$ out of $x^{3}$ .

$x \cdot x^{2} - 12 x^{2} + 27 x = 0$

Factor $x$ out of $- 12 x^{2}$ .

$x \cdot x^{2} + x (- 12 x) + 27 x = 0$

Factor $x$ out of $27 x$ .

$x \cdot x^{2} + x (- 12 x) + x \cdot 27 = 0$

Factor $x$ out of $x \cdot x^{2} + x (- 12 x)$ .

$x (x^{2} - 12 x) + x \cdot 27 = 0$

Factor $x$ out of $x (x^{2} - 12 x) + x \cdot 27$ .

$x (x^{2} - 12 x + 27) = 0$

Step 2

Factor.

Factor $x^{2} - 12 x + 27$ 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 $27$ and whose sum is $- 12$ .

$- 9, - 3$

Write the factored form using these integers.

$x ((x - 9) (x - 3)) = 0$

Remove unnecessary parentheses.

$x (x - 9) (x - 3) = 0$

Step 3

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

$x = 0$

$x - 9 = 0$

$x - 3 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

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

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Step 7

The final solution is all the values that make $x (x - 9) (x - 3) = 0$ true.

$x = 0, 9, 3$

Solve by Factoring x^3-12x^2+27x=0

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