Solve -7y^2+7y

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

Factor

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

Solution Steps

Factor out 7.

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

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

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

Rewrite the complete factored expression.

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

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.

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

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.

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

Take the square root of 7^{2}.

$$y=\frac{-7±7}{2\left(-7\right)}$$

Multiply 2 times -7.

$$y=\frac{-7±7}{-14}$$

Now solve the equation y=\frac{-7±7}{-14} when ± is plus. Add -7 to 7.

$$y=\frac{0}{-14}$$

Divide 0 by -14.

$$y=0$$

Now solve the equation y=\frac{-7±7}{-14} when ± is minus. Subtract 7 from -7.

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

Divide -14 by -14.

$$y=1$$

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 1 for x_{2}.

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

Evaluate

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