0=-2x^2+220x-2000

Solution for 0=-2x^2+220x-2000 equation:

Simplifying
0 = -2x2 + 220x + -2000

Reorder the terms:
0 = -2000 + 220x + -2x2

Solving
0 = -2000 + 220x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + 2000 = 2000
2000 + -220x + 2x2 = -2000 + 220x + -2x2 + 2000 + -220x + 2x2

Reorder the terms:
2000 + -220x + 2x2 = -2000 + 2000 + 220x + -220x + -2x2 + 2x2

Combine like terms: -2000 + 2000 = 0
2000 + -220x + 2x2 = 0 + 220x + -220x + -2x2 + 2x2
2000 + -220x + 2x2 = 220x + -220x + -2x2 + 2x2

Combine like terms: 220x + -220x = 0
2000 + -220x + 2x2 = 0 + -2x2 + 2x2
2000 + -220x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
2000 + -220x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1000 + -110x + x2) = 0

Factor a trinomial.
2((10 + -1x)(100 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Subproblem 2
Set the factor '(100 + -1x)' equal to zero and attempt to solve:

Simplifying
100 + -1x = 0

Solving
100 + -1x = 0

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

Add '-100' to each side of the equation.
100 + -100 + -1x = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -1x = 0 + -100
-1x = 0 + -100

Combine like terms: 0 + -100 = -100
-1x = -100

Divide each side by '-1'.
x = 100

Simplifying
x = 100
Solution
x = {10, 100}