Solve by Factoring 7x^2=21x

$7 x^{2} = 21 x$

Step 1

Subtract $21 x$ from both sides of the equation.

$7 x^{2} - 21 x = 0$

Step 2

Factor $7 x$ out of $7 x^{2} - 21 x$ .

Factor $7 x$ out of $7 x^{2}$ .

$7 x (x) - 21 x = 0$

Factor $7 x$ out of $- 21 x$ .

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

Factor $7 x$ out of $7 x (x) + 7 x (- 3)$ .

$7 x (x - 3) = 0$

Step 3

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

$x = 0$

$x - 3 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

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 6

The final solution is all the values that make $7 x (x - 3) = 0$ true.

$x = 0, 3$