Solve 26y(y-1)=0

$$26 y ( y - 1 ) = 0$$

Solve for y

$$y=1$$

$$y=0$$

Steps Using Factoring

Use the distributive property to multiply 26y by y-1.

$$26y^{2}-26y=0$$

Factor out y.

$$y\left(26y-26\right)=0$$

To find equation solutions, solve y=0 and 26y-26=0.

$$y=0 y=1$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 26y by y-1.

$$26y^{2}-26y=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 26 for a, -26 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-26\right)±\sqrt{\left(-26\right)^{2}}}{2\times 26}$$

Take the square root of \left(-26\right)^{2}.

$$y=\frac{-\left(-26\right)±26}{2\times 26}$$

The opposite of -26 is 26.

$$y=\frac{26±26}{2\times 26}$$

Multiply 2 times 26.

$$y=\frac{26±26}{52}$$

Now solve the equation y=\frac{26±26}{52} when ± is plus. Add 26 to 26.

$$y=\frac{52}{52}$$

Divide 52 by 52.

$$y=1$$

Now solve the equation y=\frac{26±26}{52} when ± is minus. Subtract 26 from 26.

$$y=\frac{0}{52}$$

Divide 0 by 52.

$$y=0$$

The equation is now solved.

$$y=1 y=0$$

Steps for Completing the Square

Use the distributive property to multiply 26y by y-1.

$$26y^{2}-26y=0$$

Divide both sides by 26.

$$\frac{26y^{2}-26y}{26}=\frac{0}{26}$$

Dividing by 26 undoes the multiplication by 26.

$$y^{2}+\left(-\frac{26}{26}\right)y=\frac{0}{26}$$

Divide -26 by 26.

$$y^{2}-y=\frac{0}{26}$$

Divide 0 by 26.

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

Divide -1, the coefficient of the x term, by 2 to get -\frac{1}{2}. Then add the square of -\frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Square -\frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$y^{2}-y+\frac{1}{4}=\frac{1}{4}$$

Factor y^{2}-y+\frac{1}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(y-\frac{1}{2}\right)^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(y-\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Simplify.

$$y-\frac{1}{2}=\frac{1}{2} y-\frac{1}{2}=-\frac{1}{2}$$

Add \frac{1}{2} to both sides of the equation.

$$y=1 y=0$$