1000=-5x^2+150x

Solution for 1000=-5x^2+150x equation:

Simplifying
1000 = -5x2 + 150x

Reorder the terms:
1000 = 150x + -5x2

Solving
1000 = 150x + -5x2

Solving for variable 'x'.

Reorder the terms:
1000 + -150x + 5x2 = 150x + -150x + -5x2 + 5x2

Combine like terms: 150x + -150x = 0
1000 + -150x + 5x2 = 0 + -5x2 + 5x2
1000 + -150x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
1000 + -150x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(200 + -30x + x2) = 0

Factor a trinomial.
5((10 + -1x)(20 + -1x)) = 0

Ignore the factor 5.
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 '(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 = {10, 20}