-2x^2+1000x=19200

Solution for -2x^2+1000x=19200 equation:

Simplifying
-2x2 + 1000x = 19200

Reorder the terms:
1000x + -2x2 = 19200

Solving
1000x + -2x2 = 19200

Solving for variable 'x'.

Reorder the terms:
-19200 + 1000x + -2x2 = 19200 + -19200

Combine like terms: 19200 + -19200 = 0
-19200 + 1000x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9600 + 500x + -1x2) = 0

Factor a trinomial.
2((-480 + x)(20 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-480 + x)' equal to zero and attempt to solve:

Simplifying
-480 + x = 0

Solving
-480 + x = 0

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

Add '480' to each side of the equation.
-480 + 480 + x = 0 + 480

Combine like terms: -480 + 480 = 0
0 + x = 0 + 480
x = 0 + 480

Combine like terms: 0 + 480 = 480
x = 480

Simplifying
x = 480
Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

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

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

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

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

Simplifying
x = 20
Solution
x = {480, 20}