(x-100)(x-50)=15000

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

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

Reorder the terms:
(-100 + x)(x + -50) = 15000

Reorder the terms:
(-100 + x)(-50 + x) = 15000

Multiply (-100 + x) * (-50 + x)
(-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)) = 15000

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

Solving
5000 + -150x + x2 = 15000

Solving for variable 'x'.

Reorder the terms:
5000 + -15000 + -150x + x2 = 15000 + -15000

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

Combine like terms: 15000 + -15000 = 0
-10000 + -150x + x2 = 0

Factor a trinomial.
(-50 + -1x)(200 + -1x) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
200 + -1x = 0

Solving
200 + -1x = 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 + -1x = 0 + -200

Combine like terms: 200 + -200 = 0
0 + -1x = 0 + -200
-1x = 0 + -200

Combine like terms: 0 + -200 = -200
-1x = -200

Divide each side by '-1'.
x = 200

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