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

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

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

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

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

Multiply (3 + x) * (1 + 2x)
(3(1 + 2x) + x(1 + 2x)) = 2(2x + -1)
((1 * 3 + 2x * 3) + x(1 + 2x)) = 2(2x + -1)
((3 + 6x) + x(1 + 2x)) = 2(2x + -1)
(3 + 6x + (1 * x + 2x * x)) = 2(2x + -1)
(3 + 6x + (1x + 2x2)) = 2(2x + -1)

Combine like terms: 6x + 1x = 7x
(3 + 7x + 2x2) = 2(2x + -1)

Reorder the terms:
3 + 7x + 2x2 = 2(-1 + 2x)
3 + 7x + 2x2 = (-1 * 2 + 2x * 2)
3 + 7x + 2x2 = (-2 + 4x)

Solving
3 + 7x + 2x2 = -2 + 4x

Solving for variable 'x'.

Reorder the terms:
3 + 2 + 7x + -4x + 2x2 = -2 + 4x + 2 + -4x

Combine like terms: 3 + 2 = 5
5 + 7x + -4x + 2x2 = -2 + 4x + 2 + -4x

Combine like terms: 7x + -4x = 3x
5 + 3x + 2x2 = -2 + 4x + 2 + -4x

Reorder the terms:
5 + 3x + 2x2 = -2 + 2 + 4x + -4x

Combine like terms: -2 + 2 = 0
5 + 3x + 2x2 = 0 + 4x + -4x
5 + 3x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
5 + 3x + 2x2 = 0

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

Divide each side by '2'.
2.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 1.5x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 1.5x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 1.5x + x2 = 0 + -2.5
1.5x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
1.5x + x2 = -2.5

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 = -2.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -2.5 + 0.5625

Combine like terms: -2.5 + 0.5625 = -1.9375
0.5625 + 1.5x + x2 = -1.9375

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = -1.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.