Solve 18x^2-24x

$$18 x ^ { 2 } - 24 x$$

Factor

$$6x\left(3x-4\right)$$

Solution Steps

Factor out 6.

$$6\left(3x^{2}-4x\right)$$

Consider 3x^{2}-4x. Factor out x.

$$x\left(3x-4\right)$$

Rewrite the complete factored expression.

$$6x\left(3x-4\right)$$

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.

$$18x^{2}-24x=0$$

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.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\times 18}$$

Take the square root of \left(-24\right)^{2}.

$$x=\frac{-\left(-24\right)±24}{2\times 18}$$

The opposite of -24 is 24.

$$x=\frac{24±24}{2\times 18}$$

Multiply 2 times 18.

$$x=\frac{24±24}{36}$$

Now solve the equation x=\frac{24±24}{36} when ± is plus. Add 24 to 24.

$$x=\frac{48}{36}$$

Reduce the fraction \frac{48}{36} to lowest terms by extracting and canceling out 12.

$$x=\frac{4}{3}$$

Now solve the equation x=\frac{24±24}{36} when ± is minus. Subtract 24 from 24.

$$x=\frac{0}{36}$$

Divide 0 by 36.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{4}{3} for x_{1} and 0 for x_{2}.

$$18x^{2}-24x=18\left(x-\frac{4}{3}\right)x$$

Subtract \frac{4}{3} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$18x^{2}-24x=18\times \frac{3x-4}{3}x$$

Cancel out 3, the greatest common factor in 18 and 3.

$$18x^{2}-24x=6\left(3x-4\right)x$$

Evaluate

$$6x\left(3x-4\right)$$