1000=-2x^2+120x

Solution for 1000=-2x^2+120x equation:

Simplifying
1000 = -2x2 + 120x

Reorder the terms:
1000 = 120x + -2x2

Solving
1000 = 120x + -2x2

Solving for variable 'x'.

Reorder the terms:
1000 + -120x + 2x2 = 120x + -120x + -2x2 + 2x2

Combine like terms: 120x + -120x = 0
1000 + -120x + 2x2 = 0 + -2x2 + 2x2
1000 + -120x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
1000 + -120x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(500 + -60x + x2) = 0

Factor a trinomial.
2((10 + -1x)(50 + -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 '(50 + -1x)' equal to zero and attempt to solve:

Simplifying
50 + -1x = 0

Solving
50 + -1x = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1x = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1x = 0 + -50
-1x = 0 + -50

Combine like terms: 0 + -50 = -50
-1x = -50

Divide each side by '-1'.
x = 50

Simplifying
x = 50
Solution
x = {10, 50}