(x+80)(x+120)=16500

Solution for (x+80)(x+120)=16500 equation:

Simplifying
(x + 80)(x + 120) = 16500

Reorder the terms:
(80 + x)(x + 120) = 16500

Reorder the terms:
(80 + x)(120 + x) = 16500

Multiply (80 + x) * (120 + x)
(80(120 + x) + x(120 + x)) = 16500
((120 * 80 + x * 80) + x(120 + x)) = 16500
((9600 + 80x) + x(120 + x)) = 16500
(9600 + 80x + (120 * x + x * x)) = 16500
(9600 + 80x + (120x + x2)) = 16500

Combine like terms: 80x + 120x = 200x
(9600 + 200x + x2) = 16500

Solving
9600 + 200x + x2 = 16500

Solving for variable 'x'.

Reorder the terms:
9600 + -16500 + 200x + x2 = 16500 + -16500

Combine like terms: 9600 + -16500 = -6900
-6900 + 200x + x2 = 16500 + -16500

Combine like terms: 16500 + -16500 = 0
-6900 + 200x + x2 = 0

Factor a trinomial.
(-230 + -1x)(30 + -1x) = 0

Subproblem 1
Set the factor '(-230 + -1x)' equal to zero and attempt to solve:

Simplifying
-230 + -1x = 0

Solving
-230 + -1x = 0

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

Add '230' to each side of the equation.
-230 + 230 + -1x = 0 + 230

Combine like terms: -230 + 230 = 0
0 + -1x = 0 + 230
-1x = 0 + 230

Combine like terms: 0 + 230 = 230
-1x = 230

Divide each side by '-1'.
x = -230

Simplifying
x = -230
Subproblem 2
Set the factor '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Solution
x = {-230, 30}