3X(2X+2)=2X-1(3X+6)

Solution for 3X(2X+2)=2X-1(3X+6) equation:

Simplifying
3X(2X + 2) = 2X + -1(3X + 6)

Reorder the terms:
3X(2 + 2X) = 2X + -1(3X + 6)
(2 * 3X + 2X * 3X) = 2X + -1(3X + 6)
(6X + 6X2) = 2X + -1(3X + 6)

Reorder the terms:
6X + 6X2 = 2X + -1(6 + 3X)
6X + 6X2 = 2X + (6 * -1 + 3X * -1)
6X + 6X2 = 2X + (-6 + -3X)

Reorder the terms:
6X + 6X2 = -6 + 2X + -3X

Combine like terms: 2X + -3X = -1X
6X + 6X2 = -6 + -1X

Solving
6X + 6X2 = -6 + -1X

Solving for variable 'X'.

Reorder the terms:
6 + 6X + X + 6X2 = -6 + -1X + 6 + X

Combine like terms: 6X + X = 7X
6 + 7X + 6X2 = -6 + -1X + 6 + X

Reorder the terms:
6 + 7X + 6X2 = -6 + 6 + -1X + X

Combine like terms: -6 + 6 = 0
6 + 7X + 6X2 = 0 + -1X + X
6 + 7X + 6X2 = -1X + X

Combine like terms: -1X + X = 0
6 + 7X + 6X2 = 0

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

Divide each side by '6'.
1 + 1.166666667X + X2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 1.166666667X + -1 + X2 = 0 + -1

Reorder the terms:
1 + -1 + 1.166666667X + X2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 1.166666667X + X2 = 0 + -1
1.166666667X + X2 = 0 + -1

Combine like terms: 0 + -1 = -1
1.166666667X + X2 = -1

The X term is 1.166666667X.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667X + 0.3402777780 + X2 = -1 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667X + X2 = -1 + 0.3402777780

Combine like terms: -1 + 0.3402777780 = -0.659722222
0.3402777780 + 1.166666667X + X2 = -0.659722222

Factor a perfect square on the left side:
(X + 0.5833333335)(X + 0.5833333335) = -0.659722222

Can't calculate square root of the right side.

The solution to this equation could not be determined.