Solve 8y^2-20y=

$$8 y ^ { 2 } - 20 y =$$

Factor

$$4y\left(2y-5\right)$$

Solution Steps

Factor out 4.

$$4\left(2y^{2}-5y\right)$$

Consider 2y^{2}-5y. Factor out y.

$$y\left(2y-5\right)$$

Rewrite the complete factored expression.

$$4y\left(2y-5\right)$$

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.

$$8y^{2}-20y=0$$

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.

$$y=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}}}{2\times 8}$$

Take the square root of \left(-20\right)^{2}.

$$y=\frac{-\left(-20\right)±20}{2\times 8}$$

The opposite of -20 is 20.

$$y=\frac{20±20}{2\times 8}$$

Multiply 2 times 8.

$$y=\frac{20±20}{16}$$

Now solve the equation y=\frac{20±20}{16} when ± is plus. Add 20 to 20.

$$y=\frac{40}{16}$$

Reduce the fraction \frac{40}{16} to lowest terms by extracting and canceling out 8.

$$y=\frac{5}{2}$$

Now solve the equation y=\frac{20±20}{16} when ± is minus. Subtract 20 from 20.

$$y=\frac{0}{16}$$

Divide 0 by 16.

$$y=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{5}{2} for x_{1} and 0 for x_{2}.

$$8y^{2}-20y=8\left(y-\frac{5}{2}\right)y$$

Subtract \frac{5}{2} from y by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$8y^{2}-20y=8\times \frac{2y-5}{2}y$$

Cancel out 2, the greatest common factor in 8 and 2.

$$8y^{2}-20y=4\left(2y-5\right)y$$

Evaluate

$$4y\left(2y-5\right)$$