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

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

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

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

Reorder the terms:
3x + 3x2 = 2(-3 + x)
3x + 3x2 = (-3 * 2 + x * 2)
3x + 3x2 = (-6 + 2x)

Solving
3x + 3x2 = -6 + 2x

Solving for variable 'x'.

Reorder the terms:
6 + 3x + -2x + 3x2 = -6 + 2x + 6 + -2x

Combine like terms: 3x + -2x = 1x
6 + 1x + 3x2 = -6 + 2x + 6 + -2x

Reorder the terms:
6 + 1x + 3x2 = -6 + 6 + 2x + -2x

Combine like terms: -6 + 6 = 0
6 + 1x + 3x2 = 0 + 2x + -2x
6 + 1x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
6 + 1x + 3x2 = 0

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

Divide each side by '3'.
2 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 0.3333333333x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 0.3333333333x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 0.3333333333x + x2 = 0 + -2
0.3333333333x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
0.3333333333x + x2 = -2

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = -2 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = -2 + 0.02777777779

Combine like terms: -2 + 0.02777777779 = -1.97222222221
0.02777777779 + 0.3333333333x + x2 = -1.97222222221

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = -1.97222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.