Solve for y y^2-2y+1y=101y

$y^{2} - 2 y + 1 y = 101 y$

Step 1

Simplify $y^{2} - 2 y + 1 y$ .

Multiply $y$ by $1$ .

$y^{2} - 2 y + y = 101 y$

Add $- 2 y$ and $y$ .

$y^{2} - y = 101 y$

Step 2

Move all terms containing $y$ to the left side of the equation.

Subtract $101 y$ from both sides of the equation.

$y^{2} - y - 101 y = 0$

Subtract $101 y$ from $- y$ .

$y^{2} - 102 y = 0$

Step 3

Factor $y$ out of $y^{2} - 102 y$ .

Factor $y$ out of $y^{2}$ .

$y \cdot y - 102 y = 0$

Factor $y$ out of $- 102 y$ .

$y \cdot y + y \cdot - 102 = 0$

Factor $y$ out of $y \cdot y + y \cdot - 102$ .

$y (y - 102) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$y = 0$

$y - 102 = 0$

Step 5

Set $y$ equal to $0$ .

$y = 0$

Step 6

Set $y - 102$ equal to $0$ and solve for $y$ .

Set $y - 102$ equal to $0$ .

$y - 102 = 0$

Add $102$ to both sides of the equation.

$y = 102$

Step 7

The final solution is all the values that make $y (y - 102) = 0$ true.

$y = 0, 102$