200x-2x^2=-x^2+5x+4950

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Solution for 200x-2x^2=-x^2+5x+4950 equation: 


Simplifying
200x + -2x2 = -1x2 + 5x + 4950

Reorder the terms:
200x + -2x2 = 4950 + 5x + -1x2

Solving
200x + -2x2 = 4950 + 5x + -1x2

Solving for variable 'x'.

Reorder the terms:
-4950 + 200x + -5x + -2x2 + x2 = 4950 + 5x + -1x2 + -4950 + -5x + x2

Combine like terms: 200x + -5x = 195x
-4950 + 195x + -2x2 + x2 = 4950 + 5x + -1x2 + -4950 + -5x + x2

Combine like terms: -2x2 + x2 = -1x2
-4950 + 195x + -1x2 = 4950 + 5x + -1x2 + -4950 + -5x + x2

Reorder the terms:
-4950 + 195x + -1x2 = 4950 + -4950 + 5x + -5x + -1x2 + x2

Combine like terms: 4950 + -4950 = 0
-4950 + 195x + -1x2 = 0 + 5x + -5x + -1x2 + x2
-4950 + 195x + -1x2 = 5x + -5x + -1x2 + x2

Combine like terms: 5x + -5x = 0
-4950 + 195x + -1x2 = 0 + -1x2 + x2
-4950 + 195x + -1x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-4950 + 195x + -1x2 = 0

Factor a trinomial.
(-165 + x)(30 + -1x) = 0


Subproblem 1
Set the factor '(-165 + x)' equal to zero and attempt to solve:

Simplifying
-165 + x = 0

Solving
-165 + x = 0

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

Add '165' to each side of the equation.
-165 + 165 + x = 0 + 165

Combine like terms: -165 + 165 = 0
0 + x = 0 + 165
x = 0 + 165

Combine like terms: 0 + 165 = 165
x = 165

Simplifying
x = 165

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 = {165, 30}

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