(X+1)2+(x+2)2=(2x+1)(x+1)

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Solution for (X+1)2+(x+2)2=(2x+1)(x+1) equation: 


Simplifying
(X + 1) * 2 + (x + 2) * 2 = (2x + 1)(x + 1)

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

Reorder the terms for easier multiplication:
2(1 + X) + (x + 2) * 2 = (2x + 1)(x + 1)
(1 * 2 + X * 2) + (x + 2) * 2 = (2x + 1)(x + 1)
(2 + 2X) + (x + 2) * 2 = (2x + 1)(x + 1)

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

Reorder the terms for easier multiplication:
2 + 2X + 2(2 + x) = (2x + 1)(x + 1)
2 + 2X + (2 * 2 + x * 2) = (2x + 1)(x + 1)
2 + 2X + (4 + 2x) = (2x + 1)(x + 1)

Reorder the terms:
2 + 4 + 2X + 2x = (2x + 1)(x + 1)

Combine like terms: 2 + 4 = 6
6 + 2X + 2x = (2x + 1)(x + 1)

Reorder the terms:
6 + 2X + 2x = (1 + 2x)(x + 1)

Reorder the terms:
6 + 2X + 2x = (1 + 2x)(1 + x)

Multiply (1 + 2x) * (1 + x)
6 + 2X + 2x = (1(1 + x) + 2x * (1 + x))
6 + 2X + 2x = ((1 * 1 + x * 1) + 2x * (1 + x))
6 + 2X + 2x = ((1 + 1x) + 2x * (1 + x))
6 + 2X + 2x = (1 + 1x + (1 * 2x + x * 2x))
6 + 2X + 2x = (1 + 1x + (2x + 2x2))

Combine like terms: 1x + 2x = 3x
6 + 2X + 2x = (1 + 3x + 2x2)

Solving
6 + 2X + 2x = 1 + 3x + 2x2

Solving for variable 'X'.

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

Add '-6' to each side of the equation.
6 + 2X + -6 + 2x = 1 + 3x + -6 + 2x2

Reorder the terms:
6 + -6 + 2X + 2x = 1 + 3x + -6 + 2x2

Combine like terms: 6 + -6 = 0
0 + 2X + 2x = 1 + 3x + -6 + 2x2
2X + 2x = 1 + 3x + -6 + 2x2

Reorder the terms:
2X + 2x = 1 + -6 + 3x + 2x2

Combine like terms: 1 + -6 = -5
2X + 2x = -5 + 3x + 2x2

Add '-2x' to each side of the equation.
2X + 2x + -2x = -5 + 3x + -2x + 2x2

Combine like terms: 2x + -2x = 0
2X + 0 = -5 + 3x + -2x + 2x2
2X = -5 + 3x + -2x + 2x2

Combine like terms: 3x + -2x = 1x
2X = -5 + 1x + 2x2

Divide each side by '2'.
X = -2.5 + 0.5x + x2

Simplifying
X = -2.5 + 0.5x + x2

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