y(y-1)=56

Solution for y(y-1)=56 equation:

Simplifying
y(y + -1) = 56

Reorder the terms:
y(-1 + y) = 56
(-1 * y + y * y) = 56
(-1y + y2) = 56

Solving
-1y + y2 = 56

Solving for variable 'y'.

Reorder the terms:
-56 + -1y + y2 = 56 + -56

Combine like terms: 56 + -56 = 0
-56 + -1y + y2 = 0

Factor a trinomial.
(-7 + -1y)(8 + -1y) = 0

Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve:

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y = 0 + 7
-1y = 0 + 7

Combine like terms: 0 + 7 = 7
-1y = 7

Divide each side by '-1'.
y = -7

Simplifying
y = -7
Subproblem 2
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8
Solution
y = {-7, 8}