Solve -3x(5x-3)=0

$$-3x(5x-3)=0$$

Solve for x

$$x=\frac{3}{5}=0.6$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply -3x by 5x-3.

$$-15x^{2}+9x=0$$

Factor out x.

$$x\left(-15x+9\right)=0$$

To find equation solutions, solve x=0 and -15x+9=0.

$$x=0 x=\frac{3}{5}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply -3x by 5x-3.

$$-15x^{2}+9x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -15 for a, 9 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-9±\sqrt{9^{2}}}{2\left(-15\right)}$$

Take the square root of 9^{2}.

$$x=\frac{-9±9}{2\left(-15\right)}$$

Multiply 2 times -15.

$$x=\frac{-9±9}{-30}$$

Now solve the equation x=\frac{-9±9}{-30} when ± is plus. Add -9 to 9.

$$x=\frac{0}{-30}$$

Divide 0 by -30.

$$x=0$$

Now solve the equation x=\frac{-9±9}{-30} when ± is minus. Subtract 9 from -9.

$$x=-\frac{18}{-30}$$

Reduce the fraction \frac{-18}{-30} to lowest terms by extracting and canceling out 6.

$$x=\frac{3}{5}$$

The equation is now solved.

$$x=0 x=\frac{3}{5}$$

Steps for Completing the Square

Use the distributive property to multiply -3x by 5x-3.

$$-15x^{2}+9x=0$$

Divide both sides by -15.

$$\frac{-15x^{2}+9x}{-15}=\frac{0}{-15}$$

Dividing by -15 undoes the multiplication by -15.

$$x^{2}+\frac{9}{-15}x=\frac{0}{-15}$$

Reduce the fraction \frac{9}{-15} to lowest terms by extracting and canceling out 3.

$$x^{2}-\frac{3}{5}x=\frac{0}{-15}$$

Divide 0 by -15.

$$x^{2}-\frac{3}{5}x=0$$

Divide -\frac{3}{5}, the coefficient of the x term, by 2 to get -\frac{3}{10}. Then add the square of -\frac{3}{10} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{3}{5}x+\left(-\frac{3}{10}\right)^{2}=\left(-\frac{3}{10}\right)^{2}$$

Square -\frac{3}{10} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{3}{5}x+\frac{9}{100}=\frac{9}{100}$$

Factor x^{2}-\frac{3}{5}x+\frac{9}{100}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{3}{10}\right)^{2}=\frac{9}{100}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{3}{10}\right)^{2}}=\sqrt{\frac{9}{100}}$$

Simplify.

$$x-\frac{3}{10}=\frac{3}{10} x-\frac{3}{10}=-\frac{3}{10}$$

Add \frac{3}{10} to both sides of the equation.

$$x=\frac{3}{5} x=0$$