(120+X)(80+X)=16500

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


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

Multiply (120 + X) * (80 + X)
(120(80 + X) + X(80 + X)) = 16500
((80 * 120 + X * 120) + X(80 + X)) = 16500
((9600 + 120X) + X(80 + X)) = 16500
(9600 + 120X + (80 * X + X * X)) = 16500
(9600 + 120X + (80X + X2)) = 16500

Combine like terms: 120X + 80X = 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}

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