Solve 21x^2-7x

$$21 x ^ { 2 } - 7 x$$

Factor

$$7x\left(3x-1\right)$$

Solution Steps

Factor out 7.

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

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

$$x\left(3x-1\right)$$

Rewrite the complete factored expression.

$$7x\left(3x-1\right)$$

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.

$$21x^{2}-7x=0$$

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.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}}}{2\times 21}$$

Take the square root of \left(-7\right)^{2}.

$$x=\frac{-\left(-7\right)±7}{2\times 21}$$

The opposite of -7 is 7.

$$x=\frac{7±7}{2\times 21}$$

Multiply 2 times 21.

$$x=\frac{7±7}{42}$$

Now solve the equation x=\frac{7±7}{42} when ± is plus. Add 7 to 7.

$$x=\frac{14}{42}$$

Reduce the fraction \frac{14}{42} to lowest terms by extracting and canceling out 14.

$$x=\frac{1}{3}$$

Now solve the equation x=\frac{7±7}{42} when ± is minus. Subtract 7 from 7.

$$x=\frac{0}{42}$$

Divide 0 by 42.

$$x=0$$

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

$$21x^{2}-7x=21\left(x-\frac{1}{3}\right)x$$

Subtract \frac{1}{3} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$21x^{2}-7x=21\times \frac{3x-1}{3}x$$

Cancel out 3, the greatest common factor in 21 and 3.

$$21x^{2}-7x=7\left(3x-1\right)x$$

Evaluate

$$7x\left(3x-1\right)$$