Solve 7x^2-21x=

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

Factor

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

Solution Steps

Factor out 7.

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

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

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

Rewrite the complete factored expression.

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

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.

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

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.

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

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

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

The opposite of -21 is 21.

$$x=\frac{21±21}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{21±21}{14}$$

Now solve the equation x=\frac{21±21}{14} when ± is plus. Add 21 to 21.

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

Divide 42 by 14.

$$x=3$$

Now solve the equation x=\frac{21±21}{14} when ± is minus. Subtract 21 from 21.

$$x=\frac{0}{14}$$

Divide 0 by 14.

$$x=0$$

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

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

Evaluate

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