(X+2)(X+1)=(X+1)(-X+3)

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Solution for (X+2)(X+1)=(X+1)(-X+3) equation: 


Simplifying
(X + 2)(X + 1) = (X + 1)(-1X + 3)

Reorder the terms:
(2 + X)(X + 1) = (X + 1)(-1X + 3)

Reorder the terms:
(2 + X)(1 + X) = (X + 1)(-1X + 3)

Multiply (2 + X) * (1 + X)
(2(1 + X) + X(1 + X)) = (X + 1)(-1X + 3)
((1 * 2 + X * 2) + X(1 + X)) = (X + 1)(-1X + 3)
((2 + 2X) + X(1 + X)) = (X + 1)(-1X + 3)
(2 + 2X + (1 * X + X * X)) = (X + 1)(-1X + 3)
(2 + 2X + (1X + X2)) = (X + 1)(-1X + 3)

Combine like terms: 2X + 1X = 3X
(2 + 3X + X2) = (X + 1)(-1X + 3)

Reorder the terms:
2 + 3X + X2 = (1 + X)(-1X + 3)

Reorder the terms:
2 + 3X + X2 = (1 + X)(3 + -1X)

Multiply (1 + X) * (3 + -1X)
2 + 3X + X2 = (1(3 + -1X) + X(3 + -1X))
2 + 3X + X2 = ((3 * 1 + -1X * 1) + X(3 + -1X))
2 + 3X + X2 = ((3 + -1X) + X(3 + -1X))
2 + 3X + X2 = (3 + -1X + (3 * X + -1X * X))
2 + 3X + X2 = (3 + -1X + (3X + -1X2))

Combine like terms: -1X + 3X = 2X
2 + 3X + X2 = (3 + 2X + -1X2)

Solving
2 + 3X + X2 = 3 + 2X + -1X2

Solving for variable 'X'.

Reorder the terms:
2 + -3 + 3X + -2X + X2 + X2 = 3 + 2X + -1X2 + -3 + -2X + X2

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

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

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

Reorder the terms:
-1 + 1X + 2X2 = 3 + -3 + 2X + -2X + -1X2 + X2

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

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

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

Factor a trinomial.
(-1 + -1X)(1 + -2X) = 0


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

Simplifying
-1 + -1X = 0

Solving
-1 + -1X = 0

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

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

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

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

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

Simplifying
X = -1

Subproblem 2
Set the factor '(1 + -2X)' equal to zero and attempt to solve:

Simplifying
1 + -2X = 0

Solving
1 + -2X = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2X = 0 + -1

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

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

Divide each side by '-2'.
X = 0.5

Simplifying
X = 0.5
Solution
X = {-1, 0.5}

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