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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

Combine like terms: 3x + -3x = 0
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.