Solve 7x-21x^2=

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

Factor

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

Solution Steps

Factor out 7.

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

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

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

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.

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

Take the square root of 7^{2}.

$$x=\frac{-7±7}{2\left(-21\right)}$$

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.

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

Divide 0 by -42.

$$x=0$$

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

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

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

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

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

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

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

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

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

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

Evaluate

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