(x-1)*(x-1)+(x+4)*(x+4)=(x-2)*(x-2)+(x+3)*(x+3)

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Solution for (x-1)*(x-1)+(x+4)*(x+4)=(x-2)*(x-2)+(x+3)*(x+3) equation: 


Simplifying
(x + -1)(x + -1) + (x + 4)(x + 4) = (x + -2)(x + -2) + (x + 3)(x + 3)

Reorder the terms:
(-1 + x)(x + -1) + (x + 4)(x + 4) = (x + -2)(x + -2) + (x + 3)(x + 3)

Reorder the terms:
(-1 + x)(-1 + x) + (x + 4)(x + 4) = (x + -2)(x + -2) + (x + 3)(x + 3)

Multiply (-1 + x) * (-1 + x)
(-1(-1 + x) + x(-1 + x)) + (x + 4)(x + 4) = (x + -2)(x + -2) + (x + 3)(x + 3)
((-1 * -1 + x * -1) + x(-1 + x)) + (x + 4)(x + 4) = (x + -2)(x + -2) + (x + 3)(x + 3)
((1 + -1x) + x(-1 + x)) + (x + 4)(x + 4) = (x + -2)(x + -2) + (x + 3)(x + 3)
(1 + -1x + (-1 * x + x * x)) + (x + 4)(x + 4) = (x + -2)(x + -2) + (x + 3)(x + 3)
(1 + -1x + (-1x + x2)) + (x + 4)(x + 4) = (x + -2)(x + -2) + (x + 3)(x + 3)

Combine like terms: -1x + -1x = -2x
(1 + -2x + x2) + (x + 4)(x + 4) = (x + -2)(x + -2) + (x + 3)(x + 3)

Reorder the terms:
1 + -2x + x2 + (4 + x)(x + 4) = (x + -2)(x + -2) + (x + 3)(x + 3)

Reorder the terms:
1 + -2x + x2 + (4 + x)(4 + x) = (x + -2)(x + -2) + (x + 3)(x + 3)

Multiply (4 + x) * (4 + x)
1 + -2x + x2 + (4(4 + x) + x(4 + x)) = (x + -2)(x + -2) + (x + 3)(x + 3)
1 + -2x + x2 + ((4 * 4 + x * 4) + x(4 + x)) = (x + -2)(x + -2) + (x + 3)(x + 3)
1 + -2x + x2 + ((16 + 4x) + x(4 + x)) = (x + -2)(x + -2) + (x + 3)(x + 3)
1 + -2x + x2 + (16 + 4x + (4 * x + x * x)) = (x + -2)(x + -2) + (x + 3)(x + 3)
1 + -2x + x2 + (16 + 4x + (4x + x2)) = (x + -2)(x + -2) + (x + 3)(x + 3)

Combine like terms: 4x + 4x = 8x
1 + -2x + x2 + (16 + 8x + x2) = (x + -2)(x + -2) + (x + 3)(x + 3)

Reorder the terms:
1 + 16 + -2x + 8x + x2 + x2 = (x + -2)(x + -2) + (x + 3)(x + 3)

Combine like terms: 1 + 16 = 17
17 + -2x + 8x + x2 + x2 = (x + -2)(x + -2) + (x + 3)(x + 3)

Combine like terms: -2x + 8x = 6x
17 + 6x + x2 + x2 = (x + -2)(x + -2) + (x + 3)(x + 3)

Combine like terms: x2 + x2 = 2x2
17 + 6x + 2x2 = (x + -2)(x + -2) + (x + 3)(x + 3)

Reorder the terms:
17 + 6x + 2x2 = (-2 + x)(x + -2) + (x + 3)(x + 3)

Reorder the terms:
17 + 6x + 2x2 = (-2 + x)(-2 + x) + (x + 3)(x + 3)

Multiply (-2 + x) * (-2 + x)
17 + 6x + 2x2 = (-2(-2 + x) + x(-2 + x)) + (x + 3)(x + 3)
17 + 6x + 2x2 = ((-2 * -2 + x * -2) + x(-2 + x)) + (x + 3)(x + 3)
17 + 6x + 2x2 = ((4 + -2x) + x(-2 + x)) + (x + 3)(x + 3)
17 + 6x + 2x2 = (4 + -2x + (-2 * x + x * x)) + (x + 3)(x + 3)
17 + 6x + 2x2 = (4 + -2x + (-2x + x2)) + (x + 3)(x + 3)

Combine like terms: -2x + -2x = -4x
17 + 6x + 2x2 = (4 + -4x + x2) + (x + 3)(x + 3)

Reorder the terms:
17 + 6x + 2x2 = 4 + -4x + x2 + (3 + x)(x + 3)

Reorder the terms:
17 + 6x + 2x2 = 4 + -4x + x2 + (3 + x)(3 + x)

Multiply (3 + x) * (3 + x)
17 + 6x + 2x2 = 4 + -4x + x2 + (3(3 + x) + x(3 + x))
17 + 6x + 2x2 = 4 + -4x + x2 + ((3 * 3 + x * 3) + x(3 + x))
17 + 6x + 2x2 = 4 + -4x + x2 + ((9 + 3x) + x(3 + x))
17 + 6x + 2x2 = 4 + -4x + x2 + (9 + 3x + (3 * x + x * x))
17 + 6x + 2x2 = 4 + -4x + x2 + (9 + 3x + (3x + x2))

Combine like terms: 3x + 3x = 6x
17 + 6x + 2x2 = 4 + -4x + x2 + (9 + 6x + x2)

Reorder the terms:
17 + 6x + 2x2 = 4 + 9 + -4x + 6x + x2 + x2

Combine like terms: 4 + 9 = 13
17 + 6x + 2x2 = 13 + -4x + 6x + x2 + x2

Combine like terms: -4x + 6x = 2x
17 + 6x + 2x2 = 13 + 2x + x2 + x2

Combine like terms: x2 + x2 = 2x2
17 + 6x + 2x2 = 13 + 2x + 2x2

Add '-2x2' to each side of the equation.
17 + 6x + 2x2 + -2x2 = 13 + 2x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
17 + 6x + 0 = 13 + 2x + 2x2 + -2x2
17 + 6x = 13 + 2x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
17 + 6x = 13 + 2x + 0
17 + 6x = 13 + 2x

Solving
17 + 6x = 13 + 2x

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
17 + 6x + -2x = 13 + 2x + -2x

Combine like terms: 6x + -2x = 4x
17 + 4x = 13 + 2x + -2x

Combine like terms: 2x + -2x = 0
17 + 4x = 13 + 0
17 + 4x = 13

Add '-17' to each side of the equation.
17 + -17 + 4x = 13 + -17

Combine like terms: 17 + -17 = 0
0 + 4x = 13 + -17
4x = 13 + -17

Combine like terms: 13 + -17 = -4
4x = -4

Divide each side by '4'.
x = -1

Simplifying
x = -1

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