(55-y)*y=684

Solution for (55-y)*y=684 equation:

Simplifying
(55 + -1y) * y = 684

Reorder the terms for easier multiplication:
y(55 + -1y) = 684
(55 * y + -1y * y) = 684
(55y + -1y2) = 684

Solving
55y + -1y2 = 684

Solving for variable 'y'.

Reorder the terms:
-684 + 55y + -1y2 = 684 + -684

Combine like terms: 684 + -684 = 0
-684 + 55y + -1y2 = 0

Factor a trinomial.
(-36 + y)(19 + -1y) = 0

Subproblem 1
Set the factor '(-36 + y)' equal to zero and attempt to solve:

Simplifying
-36 + y = 0

Solving
-36 + y = 0

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

Add '36' to each side of the equation.
-36 + 36 + y = 0 + 36

Combine like terms: -36 + 36 = 0
0 + y = 0 + 36
y = 0 + 36

Combine like terms: 0 + 36 = 36
y = 36

Simplifying
y = 36
Subproblem 2
Set the factor '(19 + -1y)' equal to zero and attempt to solve:

Simplifying
19 + -1y = 0

Solving
19 + -1y = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1y = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1y = 0 + -19
-1y = 0 + -19

Combine like terms: 0 + -19 = -19
-1y = -19

Divide each side by '-1'.
y = 19

Simplifying
y = 19
Solution
y = {36, 19}