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

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


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

Reorder the terms for easier multiplication:
1x + -1x2 + 2(2 + -1x) + (3 + x) * 2 + -1 = (x + -1)(4 + -1x) + (2x + 1)(2 + x)
1x + -1x2 + (2 * 2 + -1x * 2) + (3 + x) * 2 + -1 = (x + -1)(4 + -1x) + (2x + 1)(2 + x)
1x + -1x2 + (4 + -2x) + (3 + x) * 2 + -1 = (x + -1)(4 + -1x) + (2x + 1)(2 + x)

Reorder the terms for easier multiplication:
1x + -1x2 + 4 + -2x + 2(3 + x) + -1 = (x + -1)(4 + -1x) + (2x + 1)(2 + x)
1x + -1x2 + 4 + -2x + (3 * 2 + x * 2) + -1 = (x + -1)(4 + -1x) + (2x + 1)(2 + x)
1x + -1x2 + 4 + -2x + (6 + 2x) + -1 = (x + -1)(4 + -1x) + (2x + 1)(2 + x)

Reorder the terms:
4 + 6 + -1 + 1x + -2x + 2x + -1x2 = (x + -1)(4 + -1x) + (2x + 1)(2 + x)

Combine like terms: 4 + 6 = 10
10 + -1 + 1x + -2x + 2x + -1x2 = (x + -1)(4 + -1x) + (2x + 1)(2 + x)

Combine like terms: 10 + -1 = 9
9 + 1x + -2x + 2x + -1x2 = (x + -1)(4 + -1x) + (2x + 1)(2 + x)

Combine like terms: 1x + -2x = -1x
9 + -1x + 2x + -1x2 = (x + -1)(4 + -1x) + (2x + 1)(2 + x)

Combine like terms: -1x + 2x = 1x
9 + 1x + -1x2 = (x + -1)(4 + -1x) + (2x + 1)(2 + x)

Reorder the terms:
9 + 1x + -1x2 = (-1 + x)(4 + -1x) + (2x + 1)(2 + x)

Multiply (-1 + x) * (4 + -1x)
9 + 1x + -1x2 = (-1(4 + -1x) + x(4 + -1x)) + (2x + 1)(2 + x)
9 + 1x + -1x2 = ((4 * -1 + -1x * -1) + x(4 + -1x)) + (2x + 1)(2 + x)
9 + 1x + -1x2 = ((-4 + 1x) + x(4 + -1x)) + (2x + 1)(2 + x)
9 + 1x + -1x2 = (-4 + 1x + (4 * x + -1x * x)) + (2x + 1)(2 + x)
9 + 1x + -1x2 = (-4 + 1x + (4x + -1x2)) + (2x + 1)(2 + x)

Combine like terms: 1x + 4x = 5x
9 + 1x + -1x2 = (-4 + 5x + -1x2) + (2x + 1)(2 + x)

Reorder the terms:
9 + 1x + -1x2 = -4 + 5x + -1x2 + (1 + 2x)(2 + x)

Multiply (1 + 2x) * (2 + x)
9 + 1x + -1x2 = -4 + 5x + -1x2 + (1(2 + x) + 2x * (2 + x))
9 + 1x + -1x2 = -4 + 5x + -1x2 + ((2 * 1 + x * 1) + 2x * (2 + x))
9 + 1x + -1x2 = -4 + 5x + -1x2 + ((2 + 1x) + 2x * (2 + x))
9 + 1x + -1x2 = -4 + 5x + -1x2 + (2 + 1x + (2 * 2x + x * 2x))
9 + 1x + -1x2 = -4 + 5x + -1x2 + (2 + 1x + (4x + 2x2))

Combine like terms: 1x + 4x = 5x
9 + 1x + -1x2 = -4 + 5x + -1x2 + (2 + 5x + 2x2)

Reorder the terms:
9 + 1x + -1x2 = -4 + 2 + 5x + 5x + -1x2 + 2x2

Combine like terms: -4 + 2 = -2
9 + 1x + -1x2 = -2 + 5x + 5x + -1x2 + 2x2

Combine like terms: 5x + 5x = 10x
9 + 1x + -1x2 = -2 + 10x + -1x2 + 2x2

Combine like terms: -1x2 + 2x2 = 1x2
9 + 1x + -1x2 = -2 + 10x + 1x2

Solving
9 + 1x + -1x2 = -2 + 10x + 1x2

Solving for variable 'x'.

Reorder the terms:
9 + 2 + 1x + -10x + -1x2 + -1x2 = -2 + 10x + 1x2 + 2 + -10x + -1x2

Combine like terms: 9 + 2 = 11
11 + 1x + -10x + -1x2 + -1x2 = -2 + 10x + 1x2 + 2 + -10x + -1x2

Combine like terms: 1x + -10x = -9x
11 + -9x + -1x2 + -1x2 = -2 + 10x + 1x2 + 2 + -10x + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
11 + -9x + -2x2 = -2 + 10x + 1x2 + 2 + -10x + -1x2

Reorder the terms:
11 + -9x + -2x2 = -2 + 2 + 10x + -10x + 1x2 + -1x2

Combine like terms: -2 + 2 = 0
11 + -9x + -2x2 = 0 + 10x + -10x + 1x2 + -1x2
11 + -9x + -2x2 = 10x + -10x + 1x2 + -1x2

Combine like terms: 10x + -10x = 0
11 + -9x + -2x2 = 0 + 1x2 + -1x2
11 + -9x + -2x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
11 + -9x + -2x2 = 0

Factor a trinomial.
(1 + -1x)(11 + 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 '(11 + 2x)' equal to zero and attempt to solve:

Simplifying
11 + 2x = 0

Solving
11 + 2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + 2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2x = 0 + -11
2x = 0 + -11

Combine like terms: 0 + -11 = -11
2x = -11

Divide each side by '2'.
x = -5.5

Simplifying
x = -5.5
Solution
x = {1, -5.5}

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