-x(2x+1)=8-(3x+3)

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Solution for -x(2x+1)=8-(3x+3) equation: 


Simplifying
-1x(2x + 1) = 8 + -1(3x + 3)

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

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

Combine like terms: 8 + -3 = 5
-1x + -2x2 = 5 + -3x

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

Solving for variable 'x'.

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

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

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

Combine like terms: 5 + -5 = 0
-5 + 2x + -2x2 = 0 + -3x + 3x
-5 + 2x + -2x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-5 + 2x + -2x2 = 0

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

Divide each side by '-2'.
2.5 + -1x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -1x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -1x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -1x + x2 = 0 + -2.5
-1x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-1x + x2 = -2.5

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 = -2.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -2.5 + 0.25

Combine like terms: -2.5 + 0.25 = -2.25
0.25 + -1x + x2 = -2.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -2.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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