Solve 6y^2-24y

$$6 y ^ { 2 } - 24 y$$

Factor

$$6y\left(y-4\right)$$

Solution Steps

Factor out 6.

$$6\left(y^{2}-4y\right)$$

Consider y^{2}-4y. Factor out y.

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

Rewrite the complete factored expression.

$$6y\left(y-4\right)$$

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.

$$6y^{2}-24y=0$$

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.

$$y=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\times 6}$$

Take the square root of \left(-24\right)^{2}.

$$y=\frac{-\left(-24\right)±24}{2\times 6}$$

The opposite of -24 is 24.

$$y=\frac{24±24}{2\times 6}$$

Multiply 2 times 6.

$$y=\frac{24±24}{12}$$

Now solve the equation y=\frac{24±24}{12} when ± is plus. Add 24 to 24.

$$y=\frac{48}{12}$$

Divide 48 by 12.

$$y=4$$

Now solve the equation y=\frac{24±24}{12} when ± is minus. Subtract 24 from 24.

$$y=\frac{0}{12}$$

Divide 0 by 12.

$$y=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 4 for x_{1} and 0 for x_{2}.

$$6y^{2}-24y=6\left(y-4\right)y$$

Evaluate

$$6y\left(y-4\right)$$