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

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


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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

Combine like terms: 4 + 4 = 8
8 + 5x + -4x + x2 + x2 = -4 + 4x + -1x2 + 4 + -4x + x2

Combine like terms: 5x + -4x = 1x
8 + 1x + x2 + x2 = -4 + 4x + -1x2 + 4 + -4x + x2

Combine like terms: x2 + x2 = 2x2
8 + 1x + 2x2 = -4 + 4x + -1x2 + 4 + -4x + x2

Reorder the terms:
8 + 1x + 2x2 = -4 + 4 + 4x + -4x + -1x2 + x2

Combine like terms: -4 + 4 = 0
8 + 1x + 2x2 = 0 + 4x + -4x + -1x2 + x2
8 + 1x + 2x2 = 4x + -4x + -1x2 + x2

Combine like terms: 4x + -4x = 0
8 + 1x + 2x2 = 0 + -1x2 + x2
8 + 1x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
8 + 1x + 2x2 = 0

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

Divide each side by '2'.
4 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 0.5x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 0.5x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 0.5x + x2 = 0 + -4
0.5x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
0.5x + x2 = -4

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = -4 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -4 + 0.0625

Combine like terms: -4 + 0.0625 = -3.9375
0.0625 + 0.5x + x2 = -3.9375

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = -3.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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