12800=x^2-180x+20000

Solution for 12800=x^2-180x+20000 equation:

Simplifying
12800 = x2 + -180x + 20000

Reorder the terms:
12800 = 20000 + -180x + x2

Solving
12800 = 20000 + -180x + x2

Solving for variable 'x'.

Combine like terms: 12800 + -20000 = -7200
-7200 + 180x + -1x2 = 20000 + -180x + x2 + -20000 + 180x + -1x2

Reorder the terms:
-7200 + 180x + -1x2 = 20000 + -20000 + -180x + 180x + x2 + -1x2

Combine like terms: 20000 + -20000 = 0
-7200 + 180x + -1x2 = 0 + -180x + 180x + x2 + -1x2
-7200 + 180x + -1x2 = -180x + 180x + x2 + -1x2

Combine like terms: -180x + 180x = 0
-7200 + 180x + -1x2 = 0 + x2 + -1x2
-7200 + 180x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7200 + 180x + -1x2 = 0

Factor a trinomial.
(-120 + x)(60 + -1x) = 0

Subproblem 1
Set the factor '(-120 + x)' equal to zero and attempt to solve:

Simplifying
-120 + x = 0

Solving
-120 + x = 0

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

Add '120' to each side of the equation.
-120 + 120 + x = 0 + 120

Combine like terms: -120 + 120 = 0
0 + x = 0 + 120
x = 0 + 120

Combine like terms: 0 + 120 = 120
x = 120

Simplifying
x = 120
Subproblem 2
Set the factor '(60 + -1x)' equal to zero and attempt to solve:

Simplifying
60 + -1x = 0

Solving
60 + -1x = 0

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

Add '-60' to each side of the equation.
60 + -60 + -1x = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -1x = 0 + -60
-1x = 0 + -60

Combine like terms: 0 + -60 = -60
-1x = -60

Divide each side by '-1'.
x = 60

Simplifying
x = 60
Solution
x = {120, 60}