1200=(30+x)(20+x)

Solution for 1200=(30+x)(20+x) equation:

Simplifying
1200 = (30 + x)(20 + x)

Multiply (30 + x) * (20 + x)
1200 = (30(20 + x) + x(20 + x))
1200 = ((20 * 30 + x * 30) + x(20 + x))
1200 = ((600 + 30x) + x(20 + x))
1200 = (600 + 30x + (20 * x + x * x))
1200 = (600 + 30x + (20x + x2))

Combine like terms: 30x + 20x = 50x
1200 = (600 + 50x + x2)

Solving
1200 = 600 + 50x + x2

Solving for variable 'x'.

Combine like terms: 1200 + -600 = 600
600 + -50x + -1x2 = 600 + 50x + x2 + -600 + -50x + -1x2

Reorder the terms:
600 + -50x + -1x2 = 600 + -600 + 50x + -50x + x2 + -1x2

Combine like terms: 600 + -600 = 0
600 + -50x + -1x2 = 0 + 50x + -50x + x2 + -1x2
600 + -50x + -1x2 = 50x + -50x + x2 + -1x2

Combine like terms: 50x + -50x = 0
600 + -50x + -1x2 = 0 + x2 + -1x2
600 + -50x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
600 + -50x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(60 + x) = 0

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 '(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 = {10, -60}