40x=-x^2+6000

Solution for 40x=-x^2+6000 equation:

Simplifying
40x = -1x2 + 6000

Reorder the terms:
40x = 6000 + -1x2

Solving
40x = 6000 + -1x2

Solving for variable 'x'.

Reorder the terms:
-6000 + 40x + x2 = 6000 + -1x2 + -6000 + x2

Reorder the terms:
-6000 + 40x + x2 = 6000 + -6000 + -1x2 + x2

Combine like terms: 6000 + -6000 = 0
-6000 + 40x + x2 = 0 + -1x2 + x2
-6000 + 40x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-6000 + 40x + x2 = 0

Factor a trinomial.
(-100 + -1x)(60 + -1x) = 0

Subproblem 1
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
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 = {-100, 60}