2(x+3)=-4x(x+1)

Solution for 2(x+3)=-4x(x+1) equation:

Simplifying
2(x + 3) = -4x(x + 1)

Reorder the terms:
2(3 + x) = -4x(x + 1)
(3 * 2 + x * 2) = -4x(x + 1)
(6 + 2x) = -4x(x + 1)

Reorder the terms:
6 + 2x = -4x(1 + x)
6 + 2x = (1 * -4x + x * -4x)
6 + 2x = (-4x + -4x2)

Solving
6 + 2x = -4x + -4x2

Solving for variable 'x'.

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

Reorder the terms:
6 + 6x + 4x2 = -4x + 4x + -4x2 + 4x2

Combine like terms: -4x + 4x = 0
6 + 6x + 4x2 = 0 + -4x2 + 4x2
6 + 6x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
6 + 6x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 3x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
3 + 3x + 2x2 = 0

Solving
3 + 3x + 2x2 = 0

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

Divide each side by '2'.
1.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 1.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 1.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 1.5x + x2 = 0 + -1.5
1.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
1.5x + x2 = -1.5

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -1.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -1.5 + 0.5625

Combine like terms: -1.5 + 0.5625 = -0.9375
0.5625 + 1.5x + x2 = -0.9375

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = -0.9375

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.