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

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

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

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

Reorder the terms for easier multiplication:
2(-3 + X) + (X + 1) * 2 = (x + -2) * 2 + (X + 3)
(-3 * 2 + X * 2) + (X + 1) * 2 = (x + -2) * 2 + (X + 3)
(-6 + 2X) + (X + 1) * 2 = (x + -2) * 2 + (X + 3)

Reorder the terms:
-6 + 2X + (1 + X) * 2 = (x + -2) * 2 + (X + 3)

Reorder the terms for easier multiplication:
-6 + 2X + 2(1 + X) = (x + -2) * 2 + (X + 3)
-6 + 2X + (1 * 2 + X * 2) = (x + -2) * 2 + (X + 3)
-6 + 2X + (2 + 2X) = (x + -2) * 2 + (X + 3)

Reorder the terms:
-6 + 2 + 2X + 2X = (x + -2) * 2 + (X + 3)

Combine like terms: -6 + 2 = -4
-4 + 2X + 2X = (x + -2) * 2 + (X + 3)

Combine like terms: 2X + 2X = 4X
-4 + 4X = (x + -2) * 2 + (X + 3)

Reorder the terms:
-4 + 4X = (-2 + x) * 2 + (X + 3)

Reorder the terms for easier multiplication:
-4 + 4X = 2(-2 + x) + (X + 3)
-4 + 4X = (-2 * 2 + x * 2) + (X + 3)
-4 + 4X = (-4 + 2x) + (X + 3)

Reorder the terms:
-4 + 4X = -4 + 2x + (3 + X)

Remove parenthesis around (3 + X)
-4 + 4X = -4 + 2x + 3 + X

Reorder the terms:
-4 + 4X = -4 + 3 + X + 2x

Combine like terms: -4 + 3 = -1
-4 + 4X = -1 + X + 2x

Solving
-4 + 4X = -1 + X + 2x

Solving for variable 'X'.

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

Add '-1X' to each side of the equation.
-4 + 4X + -1X = -1 + X + -1X + 2x

Combine like terms: 4X + -1X = 3X
-4 + 3X = -1 + X + -1X + 2x

Combine like terms: X + -1X = 0
-4 + 3X = -1 + 0 + 2x
-4 + 3X = -1 + 2x

Add '4' to each side of the equation.
-4 + 4 + 3X = -1 + 4 + 2x

Combine like terms: -4 + 4 = 0
0 + 3X = -1 + 4 + 2x
3X = -1 + 4 + 2x

Combine like terms: -1 + 4 = 3
3X = 3 + 2x

Divide each side by '3'.
X = 1 + 0.6666666667x

Simplifying
X = 1 + 0.6666666667x