(X+1)*(2X-2)=X*(X+1)+(X+1)*(1-2X)

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Solution for (X+1)*(2X-2)=X*(X+1)+(X+1)*(1-2X) equation: 


Simplifying
(X + 1)(2X + -2) = X(X + 1) + (X + 1)(1 + -2X)

Reorder the terms:
(1 + X)(2X + -2) = X(X + 1) + (X + 1)(1 + -2X)

Reorder the terms:
(1 + X)(-2 + 2X) = X(X + 1) + (X + 1)(1 + -2X)

Multiply (1 + X) * (-2 + 2X)
(1(-2 + 2X) + X(-2 + 2X)) = X(X + 1) + (X + 1)(1 + -2X)
((-2 * 1 + 2X * 1) + X(-2 + 2X)) = X(X + 1) + (X + 1)(1 + -2X)
((-2 + 2X) + X(-2 + 2X)) = X(X + 1) + (X + 1)(1 + -2X)
(-2 + 2X + (-2 * X + 2X * X)) = X(X + 1) + (X + 1)(1 + -2X)
(-2 + 2X + (-2X + 2X2)) = X(X + 1) + (X + 1)(1 + -2X)

Combine like terms: 2X + -2X = 0
(-2 + 0 + 2X2) = X(X + 1) + (X + 1)(1 + -2X)
(-2 + 2X2) = X(X + 1) + (X + 1)(1 + -2X)

Reorder the terms:
-2 + 2X2 = X(1 + X) + (X + 1)(1 + -2X)
-2 + 2X2 = (1 * X + X * X) + (X + 1)(1 + -2X)
-2 + 2X2 = (1X + X2) + (X + 1)(1 + -2X)

Reorder the terms:
-2 + 2X2 = 1X + X2 + (1 + X)(1 + -2X)

Multiply (1 + X) * (1 + -2X)
-2 + 2X2 = 1X + X2 + (1(1 + -2X) + X(1 + -2X))
-2 + 2X2 = 1X + X2 + ((1 * 1 + -2X * 1) + X(1 + -2X))
-2 + 2X2 = 1X + X2 + ((1 + -2X) + X(1 + -2X))
-2 + 2X2 = 1X + X2 + (1 + -2X + (1 * X + -2X * X))
-2 + 2X2 = 1X + X2 + (1 + -2X + (1X + -2X2))

Combine like terms: -2X + 1X = -1X
-2 + 2X2 = 1X + X2 + (1 + -1X + -2X2)

Reorder the terms:
-2 + 2X2 = 1 + 1X + -1X + X2 + -2X2

Combine like terms: 1X + -1X = 0
-2 + 2X2 = 1 + 0 + X2 + -2X2
-2 + 2X2 = 1 + X2 + -2X2

Combine like terms: X2 + -2X2 = -1X2
-2 + 2X2 = 1 + -1X2

Solving
-2 + 2X2 = 1 + -1X2

Solving for variable 'X'.

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

Add 'X2' to each side of the equation.
-2 + 2X2 + X2 = 1 + -1X2 + X2

Combine like terms: 2X2 + X2 = 3X2
-2 + 3X2 = 1 + -1X2 + X2

Combine like terms: -1X2 + X2 = 0
-2 + 3X2 = 1 + 0
-2 + 3X2 = 1

Add '2' to each side of the equation.
-2 + 2 + 3X2 = 1 + 2

Combine like terms: -2 + 2 = 0
0 + 3X2 = 1 + 2
3X2 = 1 + 2

Combine like terms: 1 + 2 = 3
3X2 = 3

Divide each side by '3'.
X2 = 1

Simplifying
X2 = 1

Take the square root of each side:
X = {-1, 1}

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