(120+x)(180+x)=43200

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Solution for (120+x)(180+x)=43200 equation: 


Simplifying
(120 + x)(180 + x) = 43200

Multiply (120 + x) * (180 + x)
(120(180 + x) + x(180 + x)) = 43200
((180 * 120 + x * 120) + x(180 + x)) = 43200
((21600 + 120x) + x(180 + x)) = 43200
(21600 + 120x + (180 * x + x * x)) = 43200
(21600 + 120x + (180x + x2)) = 43200

Combine like terms: 120x + 180x = 300x
(21600 + 300x + x2) = 43200

Solving
21600 + 300x + x2 = 43200

Solving for variable 'x'.

Reorder the terms:
21600 + -43200 + 300x + x2 = 43200 + -43200

Combine like terms: 21600 + -43200 = -21600
-21600 + 300x + x2 = 43200 + -43200

Combine like terms: 43200 + -43200 = 0
-21600 + 300x + x2 = 0

Factor a trinomial.
(-360 + -1x)(60 + -1x) = 0


Subproblem 1
Set the factor '(-360 + -1x)' equal to zero and attempt to solve:

Simplifying
-360 + -1x = 0

Solving
-360 + -1x = 0

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

Add '360' to each side of the equation.
-360 + 360 + -1x = 0 + 360

Combine like terms: -360 + 360 = 0
0 + -1x = 0 + 360
-1x = 0 + 360

Combine like terms: 0 + 360 = 360
-1x = 360

Divide each side by '-1'.
x = -360

Simplifying
x = -360

Subproblem 2
Set the factor '(60 + -1x)' equal to zero and attempt to solve:

Simplifying
60 + -1x = 0

Solving
60 + -1x = 0

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

Add '-60' to each side of the equation.
60 + -60 + -1x = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -1x = 0 + -60
-1x = 0 + -60

Combine like terms: 0 + -60 = -60
-1x = -60

Divide each side by '-1'.
x = 60

Simplifying
x = 60
Solution
x = {-360, 60}

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