Solve 81x^2-21x=

$$81 { x }^{ 2 } -21x=$$

Factor

$$3x\left(27x-7\right)$$

Solution Steps

Factor out 3.

$$3\left(27x^{2}-7x\right)$$

Consider 27x^{2}-7x. Factor out x.

$$x\left(27x-7\right)$$

Rewrite the complete factored expression.

$$3x\left(27x-7\right)$$

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.

$$81x^{2}-21x=0$$

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.

$$x=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}}}{2\times 81}$$

Take the square root of \left(-21\right)^{2}.

$$x=\frac{-\left(-21\right)±21}{2\times 81}$$

The opposite of -21 is 21.

$$x=\frac{21±21}{2\times 81}$$

Multiply 2 times 81.

$$x=\frac{21±21}{162}$$

Now solve the equation x=\frac{21±21}{162} when ± is plus. Add 21 to 21.

$$x=\frac{42}{162}$$

Reduce the fraction \frac{42}{162} to lowest terms by extracting and canceling out 6.

$$x=\frac{7}{27}$$

Now solve the equation x=\frac{21±21}{162} when ± is minus. Subtract 21 from 21.

$$x=\frac{0}{162}$$

Divide 0 by 162.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{7}{27} for x_{1} and 0 for x_{2}.

$$81x^{2}-21x=81\left(x-\frac{7}{27}\right)x$$

Subtract \frac{7}{27} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$81x^{2}-21x=81\times \frac{27x-7}{27}x$$

Cancel out 27, the greatest common factor in 81 and 27.

$$81x^{2}-21x=3\left(27x-7\right)x$$

Evaluate

$$3x\left(27x-7\right)$$