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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

Divide each side by '2'.
1.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -0.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -0.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -0.5x + x2 = 0 + -1.5
-0.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-0.5x + x2 = -1.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -1.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -1.5 + 0.0625

Combine like terms: -1.5 + 0.0625 = -1.4375
0.0625 + -0.5x + x2 = -1.4375

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -1.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.