Solve by Factoring 10x^2=9x

$10 x^{2} = 9 x$

Step 1

Subtract $9 x$ from both sides of the equation.

$10 x^{2} - 9 x = 0$

Step 2

Factor $x$ out of $10 x^{2} - 9 x$ .

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

$x (10 x) - 9 x = 0$

Factor $x$ out of $- 9 x$ .

$x (10 x) + x \cdot - 9 = 0$

Factor $x$ out of $x (10 x) + x \cdot - 9$ .

$x (10 x - 9) = 0$

Step 3

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

$x = 0$

$10 x - 9 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $10 x - 9$ equal to $0$ and solve for $x$ .

Set $10 x - 9$ equal to $0$ .

$10 x - 9 = 0$

Solve $10 x - 9 = 0$ for $x$ .

Add $9$ to both sides of the equation.

$10 x = 9$

Divide each term in $10 x = 9$ by $10$ and simplify.

Divide each term in $10 x = 9$ by $10$ .

$\frac{10 x}{10} = \frac{9}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{9}{10}$

Divide $x$ by $1$ .

$x = \frac{9}{10}$

Step 6

The final solution is all the values that make $x (10 x - 9) = 0$ true.

$x = 0, \frac{9}{10}$