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

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

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

Reorder the terms:
2x(3 + x) = 2x + -1(x + 4)
(3 * 2x + x * 2x) = 2x + -1(x + 4)
(6x + 2x2) = 2x + -1(x + 4)

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

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

Combine like terms: 2x + -1x = 1x
6x + 2x2 = -4 + 1x

Solving
6x + 2x2 = -4 + 1x

Solving for variable 'x'.

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

Combine like terms: 6x + -1x = 5x
4 + 5x + 2x2 = -4 + 1x + 4 + -1x

Reorder the terms:
4 + 5x + 2x2 = -4 + 4 + 1x + -1x

Combine like terms: -4 + 4 = 0
4 + 5x + 2x2 = 0 + 1x + -1x
4 + 5x + 2x2 = 1x + -1x

Combine like terms: 1x + -1x = 0
4 + 5x + 2x2 = 0

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

Divide each side by '2'.
2 + 2.5x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 2.5x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 2.5x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2.5x + x2 = 0 + -2
2.5x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
2.5x + x2 = -2

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = -2 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = -2 + 1.5625

Combine like terms: -2 + 1.5625 = -0.4375
1.5625 + 2.5x + x2 = -0.4375

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = -0.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.