Solve 9x^2-15x

$$9 { x }^{ 2 } -15x$$

Factor

$$3x\left(3x-5\right)$$

Solution Steps

Factor out 3.

$$3\left(3x^{2}-5x\right)$$

Consider 3x^{2}-5x. Factor out x.

$$x\left(3x-5\right)$$

Rewrite the complete factored expression.

$$3x\left(3x-5\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

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

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

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

Take the square root of \left(-15\right)^{2}.

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

The opposite of -15 is 15.

$$x=\frac{15±15}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{15±15}{18}$$

Now solve the equation x=\frac{15±15}{18} when ± is plus. Add 15 to 15.

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

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

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

Now solve the equation x=\frac{15±15}{18} when ± is minus. Subtract 15 from 15.

$$x=\frac{0}{18}$$

Divide 0 by 18.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{5}{3} for x_{1} and 0 for x_{2}.

$$9x^{2}-15x=9\left(x-\frac{5}{3}\right)x$$

Subtract \frac{5}{3} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$9x^{2}-15x=9\times \frac{3x-5}{3}x$$

Cancel out 3, the greatest common factor in 9 and 3.

$$9x^{2}-15x=3\left(3x-5\right)x$$

Evaluate

$$3x\left(3x-5\right)$$