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

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

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

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

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

Solving
5000 + 150x + x2 = 8400

Solving for variable 'x'.

Reorder the terms:
5000 + -8400 + 150x + x2 = 8400 + -8400

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

Combine like terms: 8400 + -8400 = 0
-3400 + 150x + x2 = 0

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

Subproblem 1
Set the factor '(-170 + -1x)' equal to zero and attempt to solve:

Simplifying
-170 + -1x = 0

Solving
-170 + -1x = 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 + -1x = 0 + 170

Combine like terms: -170 + 170 = 0
0 + -1x = 0 + 170
-1x = 0 + 170

Combine like terms: 0 + 170 = 170
-1x = 170

Divide each side by '-1'.
x = -170

Simplifying
x = -170
Subproblem 2
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
Solution
x = {-170, 20}