(3+5x)(1-x)=((x+1)(1-2x)+3)

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Solution for (3+5x)(1-x)=((x+1)(1-2x)+3) equation: 


Simplifying
(3 + 5x)(1 + -1x) = ((x + 1)(1 + -2x) + 3)

Multiply (3 + 5x) * (1 + -1x)
(3(1 + -1x) + 5x * (1 + -1x)) = ((x + 1)(1 + -2x) + 3)
((1 * 3 + -1x * 3) + 5x * (1 + -1x)) = ((x + 1)(1 + -2x) + 3)
((3 + -3x) + 5x * (1 + -1x)) = ((x + 1)(1 + -2x) + 3)
(3 + -3x + (1 * 5x + -1x * 5x)) = ((x + 1)(1 + -2x) + 3)
(3 + -3x + (5x + -5x2)) = ((x + 1)(1 + -2x) + 3)

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

Reorder the terms:
3 + 2x + -5x2 = ((1 + x)(1 + -2x) + 3)

Multiply (1 + x) * (1 + -2x)
3 + 2x + -5x2 = ((1(1 + -2x) + x(1 + -2x)) + 3)
3 + 2x + -5x2 = (((1 * 1 + -2x * 1) + x(1 + -2x)) + 3)
3 + 2x + -5x2 = (((1 + -2x) + x(1 + -2x)) + 3)
3 + 2x + -5x2 = ((1 + -2x + (1 * x + -2x * x)) + 3)
3 + 2x + -5x2 = ((1 + -2x + (1x + -2x2)) + 3)

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

Reorder the terms:
3 + 2x + -5x2 = (1 + 3 + -1x + -2x2)

Combine like terms: 1 + 3 = 4
3 + 2x + -5x2 = (4 + -1x + -2x2)

Remove parenthesis around (4 + -1x + -2x2)
3 + 2x + -5x2 = 4 + -1x + -2x2

Solving
3 + 2x + -5x2 = 4 + -1x + -2x2

Solving for variable 'x'.

Reorder the terms:
3 + -4 + 2x + x + -5x2 + 2x2 = 4 + -1x + -2x2 + -4 + x + 2x2

Combine like terms: 3 + -4 = -1
-1 + 2x + x + -5x2 + 2x2 = 4 + -1x + -2x2 + -4 + x + 2x2

Combine like terms: 2x + x = 3x
-1 + 3x + -5x2 + 2x2 = 4 + -1x + -2x2 + -4 + x + 2x2

Combine like terms: -5x2 + 2x2 = -3x2
-1 + 3x + -3x2 = 4 + -1x + -2x2 + -4 + x + 2x2

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

Combine like terms: 4 + -4 = 0
-1 + 3x + -3x2 = 0 + -1x + x + -2x2 + 2x2
-1 + 3x + -3x2 = -1x + x + -2x2 + 2x2

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

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

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
0.3333333333 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1x + x2 = 0 + -0.3333333333
-1x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1x + x2 = -0.3333333333

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.3333333333 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.3333333333 + 0.25

Combine like terms: -0.3333333333 + 0.25 = -0.0833333333
0.25 + -1x + x2 = -0.0833333333

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -0.0833333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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