Solve by Factoring x^3-10x^2+21x=0

$x^{3} - 10 x^{2} + 21 x = 0$

Step 1

Factor $x$ out of $x^{3} - 10 x^{2} + 21 x$ .

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

$x \cdot x^{2} - 10 x^{2} + 21 x = 0$

Factor $x$ out of $- 10 x^{2}$ .

$x \cdot x^{2} + x (- 10 x) + 21 x = 0$

Factor $x$ out of $21 x$ .

$x \cdot x^{2} + x (- 10 x) + x \cdot 21 = 0$

Factor $x$ out of $x \cdot x^{2} + x (- 10 x)$ .

$x (x^{2} - 10 x) + x \cdot 21 = 0$

Factor $x$ out of $x (x^{2} - 10 x) + x \cdot 21$ .

$x (x^{2} - 10 x + 21) = 0$

Step 2

Factor.

Factor $x^{2} - 10 x + 21$ 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 $21$ and whose sum is $- 10$ .

$- 7, - 3$

Write the factored form using these integers.

$x ((x - 7) (x - 3)) = 0$

Remove unnecessary parentheses.

$x (x - 7) (x - 3) = 0$

Step 3

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

$x = 0$

$x - 7 = 0$

$x - 3 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $x - 7$ equal to $0$ and solve for $x$ .

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

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 $x (x - 7) (x - 3) = 0$ true.

$x = 0, 7, 3$

Solve by Factoring x^3-10x^2+21x=0

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