Y(50-Y)=600

Solution for Y(50-Y)=600 equation:

Simplifying
Y(50 + -1Y) = 600
(50 * Y + -1Y * Y) = 600
(50Y + -1Y2) = 600

Solving
50Y + -1Y2 = 600

Solving for variable 'Y'.

Reorder the terms:
-600 + 50Y + -1Y2 = 600 + -600

Combine like terms: 600 + -600 = 0
-600 + 50Y + -1Y2 = 0

Factor a trinomial.
(-30 + Y)(20 + -1Y) = 0

Subproblem 1
Set the factor '(-30 + Y)' equal to zero and attempt to solve:

Simplifying
-30 + Y = 0

Solving
-30 + Y = 0

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

Add '30' to each side of the equation.
-30 + 30 + Y = 0 + 30

Combine like terms: -30 + 30 = 0
0 + Y = 0 + 30
Y = 0 + 30

Combine like terms: 0 + 30 = 30
Y = 30

Simplifying
Y = 30
Subproblem 2
Set the factor '(20 + -1Y)' equal to zero and attempt to solve:

Simplifying
20 + -1Y = 0

Solving
20 + -1Y = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1Y = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1Y = 0 + -20
-1Y = 0 + -20

Combine like terms: 0 + -20 = -20
-1Y = -20

Divide each side by '-1'.
Y = 20

Simplifying
Y = 20
Solution
Y = {30, 20}