Solve by Factoring 2x^2-3x=0

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

Step 1

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

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

$x (2 x) - 3 x = 0$

Factor $x$ out of $- 3 x$ .

$x (2 x) + x \cdot - 3 = 0$

Factor $x$ out of $x (2 x) + x \cdot - 3$ .

$x (2 x - 3) = 0$

Step 2

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

$x = 0$

$2 x - 3 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $2 x - 3$ equal to $0$ and solve for $x$ .

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Solve $2 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$2 x = 3$

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 5

The final solution is all the values that make $x (2 x - 3) = 0$ true.

$x = 0, \frac{3}{2}$