120000=(200+x)(300+x)

Solution for 120000=(200+x)(300+x) equation:

Simplifying
120000 = (200 + x)(300 + x)

Multiply (200 + x) * (300 + x)
120000 = (200(300 + x) + x(300 + x))
120000 = ((300 * 200 + x * 200) + x(300 + x))
120000 = ((60000 + 200x) + x(300 + x))
120000 = (60000 + 200x + (300 * x + x * x))
120000 = (60000 + 200x + (300x + x2))

Combine like terms: 200x + 300x = 500x
120000 = (60000 + 500x + x2)

Solving
120000 = 60000 + 500x + x2

Solving for variable 'x'.

Combine like terms: 120000 + -60000 = 60000
60000 + -500x + -1x2 = 60000 + 500x + x2 + -60000 + -500x + -1x2

Reorder the terms:
60000 + -500x + -1x2 = 60000 + -60000 + 500x + -500x + x2 + -1x2

Combine like terms: 60000 + -60000 = 0
60000 + -500x + -1x2 = 0 + 500x + -500x + x2 + -1x2
60000 + -500x + -1x2 = 500x + -500x + x2 + -1x2

Combine like terms: 500x + -500x = 0
60000 + -500x + -1x2 = 0 + x2 + -1x2
60000 + -500x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
60000 + -500x + -1x2 = 0

Factor a trinomial.
(100 + -1x)(600 + 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 '(600 + x)' equal to zero and attempt to solve:

Simplifying
600 + x = 0

Solving
600 + x = 0

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

Add '-600' to each side of the equation.
600 + -600 + x = 0 + -600

Combine like terms: 600 + -600 = 0
0 + x = 0 + -600
x = 0 + -600

Combine like terms: 0 + -600 = -600
x = -600

Simplifying
x = -600
Solution
x = {100, -600}