0=1600-80X+X^2

Solution for 0=1600-80X+X^2 equation:

Simplifying
0 = 1600 + -80X + X2

Solving
0 = 1600 + -80X + X2

Solving for variable 'X'.

Combine like terms: 0 + -1600 = -1600
-1600 + 80X + -1X2 = 1600 + -80X + X2 + -1600 + 80X + -1X2

Reorder the terms:
-1600 + 80X + -1X2 = 1600 + -1600 + -80X + 80X + X2 + -1X2

Combine like terms: 1600 + -1600 = 0
-1600 + 80X + -1X2 = 0 + -80X + 80X + X2 + -1X2
-1600 + 80X + -1X2 = -80X + 80X + X2 + -1X2

Combine like terms: -80X + 80X = 0
-1600 + 80X + -1X2 = 0 + X2 + -1X2
-1600 + 80X + -1X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-1600 + 80X + -1X2 = 0

Factor a trinomial.
(-40 + X)(40 + -1X) = 0

Subproblem 1
Set the factor '(-40 + X)' equal to zero and attempt to solve:

Simplifying
-40 + X = 0

Solving
-40 + X = 0

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

Add '40' to each side of the equation.
-40 + 40 + X = 0 + 40

Combine like terms: -40 + 40 = 0
0 + X = 0 + 40
X = 0 + 40

Combine like terms: 0 + 40 = 40
X = 40

Simplifying
X = 40
Subproblem 2
Set the factor '(40 + -1X)' equal to zero and attempt to solve:

Simplifying
40 + -1X = 0

Solving
40 + -1X = 0

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

Add '-40' to each side of the equation.
40 + -40 + -1X = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -1X = 0 + -40
-1X = 0 + -40

Combine like terms: 0 + -40 = -40
-1X = -40

Divide each side by '-1'.
X = 40

Simplifying
X = 40
Solution
X = {40, 40}