-0.5x(x+2)=2(5-x)-3x

Solution for -0.5x(x+2)=2(5-x)-3x equation:

Simplifying
-0.5x(x + 2) = 2(5 + -1x) + -3x

Reorder the terms:
-0.5x(2 + x) = 2(5 + -1x) + -3x
(2 * -0.5x + x * -0.5x) = 2(5 + -1x) + -3x
(-1x + -0.5x2) = 2(5 + -1x) + -3x
-1x + -0.5x2 = (5 * 2 + -1x * 2) + -3x
-1x + -0.5x2 = (10 + -2x) + -3x

Combine like terms: -2x + -3x = -5x
-1x + -0.5x2 = 10 + -5x

Solving
-1x + -0.5x2 = 10 + -5x

Solving for variable 'x'.

Reorder the terms:
-10 + -1x + 5x + -0.5x2 = 10 + -5x + -10 + 5x

Combine like terms: -1x + 5x = 4x
-10 + 4x + -0.5x2 = 10 + -5x + -10 + 5x

Reorder the terms:
-10 + 4x + -0.5x2 = 10 + -10 + -5x + 5x

Combine like terms: 10 + -10 = 0
-10 + 4x + -0.5x2 = 0 + -5x + 5x
-10 + 4x + -0.5x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-10 + 4x + -0.5x2 = 0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
20 + -8x + x2 = 0

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -8x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -8x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -8x + x2 = 0 + -20
-8x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-8x + x2 = -20

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -20 + 16

Reorder the terms:
16 + -8x + x2 = -20 + 16

Combine like terms: -20 + 16 = -4
16 + -8x + x2 = -4

Factor a perfect square on the left side:
(x + -4)(x + -4) = -4

Can't calculate square root of the right side.

The solution to this equation could not be determined.