8400=(x+100)(x+50)

Solution for 8400=(x+100)(x+50) equation:

Simplifying
8400 = (x + 100)(x + 50)

Reorder the terms:
8400 = (100 + x)(x + 50)

Reorder the terms:
8400 = (100 + x)(50 + x)

Multiply (100 + x) * (50 + x)
8400 = (100(50 + x) + x(50 + x))
8400 = ((50 * 100 + x * 100) + x(50 + x))
8400 = ((5000 + 100x) + x(50 + x))
8400 = (5000 + 100x + (50 * x + x * x))
8400 = (5000 + 100x + (50x + x2))

Combine like terms: 100x + 50x = 150x
8400 = (5000 + 150x + x2)

Solving
8400 = 5000 + 150x + x2

Solving for variable 'x'.

Combine like terms: 8400 + -5000 = 3400
3400 + -150x + -1x2 = 5000 + 150x + x2 + -5000 + -150x + -1x2

Reorder the terms:
3400 + -150x + -1x2 = 5000 + -5000 + 150x + -150x + x2 + -1x2

Combine like terms: 5000 + -5000 = 0
3400 + -150x + -1x2 = 0 + 150x + -150x + x2 + -1x2
3400 + -150x + -1x2 = 150x + -150x + x2 + -1x2

Combine like terms: 150x + -150x = 0
3400 + -150x + -1x2 = 0 + x2 + -1x2
3400 + -150x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3400 + -150x + -1x2 = 0

Factor a trinomial.
(20 + -1x)(170 + x) = 0

Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Subproblem 2
Set the factor '(170 + x)' equal to zero and attempt to solve:

Simplifying
170 + x = 0

Solving
170 + x = 0

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

Add '-170' to each side of the equation.
170 + -170 + x = 0 + -170

Combine like terms: 170 + -170 = 0
0 + x = 0 + -170
x = 0 + -170

Combine like terms: 0 + -170 = -170
x = -170

Simplifying
x = -170
Solution
x = {20, -170}