4x-2x*(3+x)=9-x

Solution for 4x-2x*(3+x)=9-x equation:

Simplifying
4x + -2x(3 + x) = 9 + -1x
4x + (3 * -2x + x * -2x) = 9 + -1x
4x + (-6x + -2x2) = 9 + -1x

Combine like terms: 4x + -6x = -2x
-2x + -2x2 = 9 + -1x

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

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + x + 2x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(9 + x + 2x2)' equal to zero and attempt to solve:

Simplifying
9 + x + 2x2 = 0

Solving
9 + x + 2x2 = 0

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

Divide each side by '2'.
4.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 0.5x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 0.5x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 0.5x + x2 = 0 + -4.5
0.5x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
0.5x + x2 = -4.5

The x term is x.  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.
0.5x + 0.25 + x2 = -4.5 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = -4.5 + 0.25

Combine like terms: -4.5 + 0.25 = -4.25
0.25 + 0.5x + x2 = -4.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -4.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.