200(X+10)-X(X+10)=200X

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Solution for 200(X+10)-X(X+10)=200X equation: 


Simplifying
200(X + 10) + -1X(X + 10) = 200X

Reorder the terms:
200(10 + X) + -1X(X + 10) = 200X
(10 * 200 + X * 200) + -1X(X + 10) = 200X
(2000 + 200X) + -1X(X + 10) = 200X

Reorder the terms:
2000 + 200X + -1X(10 + X) = 200X
2000 + 200X + (10 * -1X + X * -1X) = 200X
2000 + 200X + (-10X + -1X2) = 200X

Combine like terms: 200X + -10X = 190X
2000 + 190X + -1X2 = 200X

Solving
2000 + 190X + -1X2 = 200X

Solving for variable 'X'.

Reorder the terms:
2000 + 190X + -200X + -1X2 = 200X + -200X

Combine like terms: 190X + -200X = -10X
2000 + -10X + -1X2 = 200X + -200X

Combine like terms: 200X + -200X = 0
2000 + -10X + -1X2 = 0

Factor a trinomial.
(40 + -1X)(50 + X) = 0


Subproblem 1
Set the factor '(40 + -1X)' equal to zero and attempt to solve:

Simplifying
40 + -1X = 0

Solving
40 + -1X = 0

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

Add '-40' to each side of the equation.
40 + -40 + -1X = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -1X = 0 + -40
-1X = 0 + -40

Combine like terms: 0 + -40 = -40
-1X = -40

Divide each side by '-1'.
X = 40

Simplifying
X = 40

Subproblem 2
Set the factor '(50 + X)' equal to zero and attempt to solve:

Simplifying
50 + X = 0

Solving
50 + X = 0

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

Add '-50' to each side of the equation.
50 + -50 + X = 0 + -50

Combine like terms: 50 + -50 = 0
0 + X = 0 + -50
X = 0 + -50

Combine like terms: 0 + -50 = -50
X = -50

Simplifying
X = -50
Solution
X = {40, -50}

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