6000=x(x-40)

Solution for 6000=x(x-40) equation:

Simplifying
6000 = x(x + -40)

Reorder the terms:
6000 = x(-40 + x)
6000 = (-40 * x + x * x)
6000 = (-40x + x2)

Solving
6000 = -40x + x2

Solving for variable 'x'.

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

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

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

Factor a trinomial.
(100 + -1x)(60 + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
60 + x = 0

Solving
60 + x = 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 + x = 0 + -60

Combine like terms: 60 + -60 = 0
0 + x = 0 + -60
x = 0 + -60

Combine like terms: 0 + -60 = -60
x = -60

Simplifying
x = -60
Solution
x = {100, -60}