Solve 18x^2-12x

$$18 { x }^{ 2 } -12x$$

Factor

$$6x\left(3x-2\right)$$

Solution Steps

Factor out 6.

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

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

$$x\left(3x-2\right)$$

Rewrite the complete factored expression.

$$6x\left(3x-2\right)$$

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.

$$18x^{2}-12x=0$$

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.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2\times 18}$$

Take the square root of \left(-12\right)^{2}.

$$x=\frac{-\left(-12\right)±12}{2\times 18}$$

The opposite of -12 is 12.

$$x=\frac{12±12}{2\times 18}$$

Multiply 2 times 18.

$$x=\frac{12±12}{36}$$

Now solve the equation x=\frac{12±12}{36} when ± is plus. Add 12 to 12.

$$x=\frac{24}{36}$$

Reduce the fraction \frac{24}{36} to lowest terms by extracting and canceling out 12.

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

Now solve the equation x=\frac{12±12}{36} when ± is minus. Subtract 12 from 12.

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

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{2}{3} for x_{1} and 0 for x_{2}.

$$18x^{2}-12x=18\left(x-\frac{2}{3}\right)x$$

Subtract \frac{2}{3} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$18x^{2}-12x=18\times \frac{3x-2}{3}x$$

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

$$18x^{2}-12x=6\left(3x-2\right)x$$

Evaluate

$$6x\left(3x-2\right)$$