40Q-Q^2=400

Solution for 40Q-Q^2=400 equation:

Simplifying
40Q + -1Q2 = 400

Solving
40Q + -1Q2 = 400

Solving for variable 'Q'.

Reorder the terms:
-400 + 40Q + -1Q2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 40Q + -1Q2 = 0

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

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

Simplifying
-20 + Q = 0

Solving
-20 + Q = 0

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

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

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

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

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

Simplifying
20 + -1Q = 0

Solving
20 + -1Q = 0

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

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

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

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

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

Simplifying
Q = 20
Solution
Q = {20, 20}