Solve -y^2+3y

$$- y ^ { 2 } + 3 y$$

Factor

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

Solution Steps

Factor out y.

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

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.

$$-y^{2}+3y=0$$

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.

$$y=\frac{-3±\sqrt{3^{2}}}{2\left(-1\right)}$$

Take the square root of 3^{2}.

$$y=\frac{-3±3}{2\left(-1\right)}$$

Multiply 2 times -1.

$$y=\frac{-3±3}{-2}$$

Now solve the equation y=\frac{-3±3}{-2} when ± is plus. Add -3 to 3.

$$y=\frac{0}{-2}$$

Divide 0 by -2.

$$y=0$$

Now solve the equation y=\frac{-3±3}{-2} when ± is minus. Subtract 3 from -3.

$$y=-\frac{6}{-2}$$

Divide -6 by -2.

$$y=3$$

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 3 for x_{2}.

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

Evaluate

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