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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