Solve 7y-21y^2

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

Factor

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

Solution Steps

Factor out 7.

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

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

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

Rewrite the complete factored expression.

$$7y\left(-3y+1\right)$$

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.

$$-21y^{2}+7y=0$$

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.

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

Take the square root of 7^{2}.

$$y=\frac{-7±7}{2\left(-21\right)}$$

Multiply 2 times -21.

$$y=\frac{-7±7}{-42}$$

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

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

Divide 0 by -42.

$$y=0$$

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

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

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

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

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}.

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

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

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

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

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

Evaluate

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