15000=(100+x)(50+x)

Solution for 15000=(100+x)(50+x) equation:

Simplifying
15000 = (100 + x)(50 + x)

Multiply (100 + x) * (50 + x)
15000 = (100(50 + x) + x(50 + x))
15000 = ((50 * 100 + x * 100) + x(50 + x))
15000 = ((5000 + 100x) + x(50 + x))
15000 = (5000 + 100x + (50 * x + x * x))
15000 = (5000 + 100x + (50x + x2))

Combine like terms: 100x + 50x = 150x
15000 = (5000 + 150x + x2)

Solving
15000 = 5000 + 150x + x2

Solving for variable 'x'.

Combine like terms: 15000 + -5000 = 10000
10000 + -150x + -1x2 = 5000 + 150x + x2 + -5000 + -150x + -1x2

Reorder the terms:
10000 + -150x + -1x2 = 5000 + -5000 + 150x + -150x + x2 + -1x2

Combine like terms: 5000 + -5000 = 0
10000 + -150x + -1x2 = 0 + 150x + -150x + x2 + -1x2
10000 + -150x + -1x2 = 150x + -150x + x2 + -1x2

Combine like terms: 150x + -150x = 0
10000 + -150x + -1x2 = 0 + x2 + -1x2
10000 + -150x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10000 + -150x + -1x2 = 0

Factor a trinomial.
(50 + -1x)(200 + x) = 0

Subproblem 1
Set the factor '(50 + -1x)' equal to zero and attempt to solve:

Simplifying
50 + -1x = 0

Solving
50 + -1x = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1x = 0 + -50

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

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

Divide each side by '-1'.
x = 50

Simplifying
x = 50
Subproblem 2
Set the factor '(200 + x)' equal to zero and attempt to solve:

Simplifying
200 + x = 0

Solving
200 + x = 0

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

Add '-200' to each side of the equation.
200 + -200 + x = 0 + -200

Combine like terms: 200 + -200 = 0
0 + x = 0 + -200
x = 0 + -200

Combine like terms: 0 + -200 = -200
x = -200

Simplifying
x = -200
Solution
x = {50, -200}