y*(40-y)=400

Solution for y*(40-y)=400 equation:

Simplifying
y(40 + -1y) = 400
(40 * y + -1y * y) = 400
(40y + -1y2) = 400

Solving
40y + -1y2 = 400

Solving for variable 'y'.

Reorder the terms:
-400 + 40y + -1y2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 40y + -1y2 = 0

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

Subproblem 1
Set the factor '(-20 + y)' equal to zero and attempt to solve:

Simplifying
-20 + y = 0

Solving
-20 + y = 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 + y = 0 + 20

Combine like terms: -20 + 20 = 0
0 + y = 0 + 20
y = 0 + 20

Combine like terms: 0 + 20 = 20
y = 20

Simplifying
y = 20
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 = {20, 20}