6000=(40+x)(x)

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

Simplifying
6000 = (40 + x)(x)

Reorder the terms for easier multiplication:
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.
(60 + -1x)(100 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(100 + x)' equal to zero and attempt to solve:

Simplifying
100 + x = 0

Solving
100 + x = 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 + x = 0 + -100

Combine like terms: 100 + -100 = 0
0 + x = 0 + -100
x = 0 + -100

Combine like terms: 0 + -100 = -100
x = -100

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