y(y+1)-1(y+1)=0

Solution for y(y+1)-1(y+1)=0 equation:

Simplifying
y(y + 1) + -1(y + 1) = 0

Reorder the terms:
y(1 + y) + -1(y + 1) = 0
(1 * y + y * y) + -1(y + 1) = 0
(1y + y2) + -1(y + 1) = 0

Reorder the terms:
1y + y2 + -1(1 + y) = 0
1y + y2 + (1 * -1 + y * -1) = 0
1y + y2 + (-1 + -1y) = 0

Reorder the terms:
-1 + 1y + -1y + y2 = 0

Combine like terms: 1y + -1y = 0
-1 + 0 + y2 = 0
-1 + y2 = 0

Solving
-1 + y2 = 0

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + y2 = 0 + 1
y2 = 0 + 1

Combine like terms: 0 + 1 = 1
y2 = 1

Simplifying
y2 = 1

Take the square root of each side:
y = {-1, 1}