200x-2x^2=-x^2+60x+2400

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Solution for 200x-2x^2=-x^2+60x+2400 equation: 


Simplifying
200x + -2x2 = -1x2 + 60x + 2400

Reorder the terms:
200x + -2x2 = 2400 + 60x + -1x2

Solving
200x + -2x2 = 2400 + 60x + -1x2

Solving for variable 'x'.

Reorder the terms:
-2400 + 200x + -60x + -2x2 + x2 = 2400 + 60x + -1x2 + -2400 + -60x + x2

Combine like terms: 200x + -60x = 140x
-2400 + 140x + -2x2 + x2 = 2400 + 60x + -1x2 + -2400 + -60x + x2

Combine like terms: -2x2 + x2 = -1x2
-2400 + 140x + -1x2 = 2400 + 60x + -1x2 + -2400 + -60x + x2

Reorder the terms:
-2400 + 140x + -1x2 = 2400 + -2400 + 60x + -60x + -1x2 + x2

Combine like terms: 2400 + -2400 = 0
-2400 + 140x + -1x2 = 0 + 60x + -60x + -1x2 + x2
-2400 + 140x + -1x2 = 60x + -60x + -1x2 + x2

Combine like terms: 60x + -60x = 0
-2400 + 140x + -1x2 = 0 + -1x2 + x2
-2400 + 140x + -1x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-2400 + 140x + -1x2 = 0

Factor a trinomial.
(-120 + x)(20 + -1x) = 0


Subproblem 1
Set the factor '(-120 + x)' equal to zero and attempt to solve:

Simplifying
-120 + x = 0

Solving
-120 + x = 0

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

Add '120' to each side of the equation.
-120 + 120 + x = 0 + 120

Combine like terms: -120 + 120 = 0
0 + x = 0 + 120
x = 0 + 120

Combine like terms: 0 + 120 = 120
x = 120

Simplifying
x = 120

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 = {120, 20}

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