Solve 9y^2-63y

$$9 y ^ { 2 } - 63 y$$

Factor

$$9y\left(y-7\right)$$

Solution Steps

Factor out 9.

$$9\left(y^{2}-7y\right)$$

Consider y^{2}-7y. Factor out y.

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

Rewrite the complete factored expression.

$$9y\left(y-7\right)$$

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.

$$9y^{2}-63y=0$$

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.

$$y=\frac{-\left(-63\right)±\sqrt{\left(-63\right)^{2}}}{2\times 9}$$

Take the square root of \left(-63\right)^{2}.

$$y=\frac{-\left(-63\right)±63}{2\times 9}$$

The opposite of -63 is 63.

$$y=\frac{63±63}{2\times 9}$$

Multiply 2 times 9.

$$y=\frac{63±63}{18}$$

Now solve the equation y=\frac{63±63}{18} when ± is plus. Add 63 to 63.

$$y=\frac{126}{18}$$

Divide 126 by 18.

$$y=7$$

Now solve the equation y=\frac{63±63}{18} when ± is minus. Subtract 63 from 63.

$$y=\frac{0}{18}$$

Divide 0 by 18.

$$y=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 7 for x_{1} and 0 for x_{2}.

$$9y^{2}-63y=9\left(y-7\right)y$$

Evaluate

$$9y\left(y-7\right)$$