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

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


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

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

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

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

Combine like terms: 2x + 3x = 5x
(3 + 5x + 2x2) = (x + -1)(2x + 1)

Reorder the terms:
3 + 5x + 2x2 = (-1 + x)(2x + 1)

Reorder the terms:
3 + 5x + 2x2 = (-1 + x)(1 + 2x)

Multiply (-1 + x) * (1 + 2x)
3 + 5x + 2x2 = (-1(1 + 2x) + x(1 + 2x))
3 + 5x + 2x2 = ((1 * -1 + 2x * -1) + x(1 + 2x))
3 + 5x + 2x2 = ((-1 + -2x) + x(1 + 2x))
3 + 5x + 2x2 = (-1 + -2x + (1 * x + 2x * x))
3 + 5x + 2x2 = (-1 + -2x + (1x + 2x2))

Combine like terms: -2x + 1x = -1x
3 + 5x + 2x2 = (-1 + -1x + 2x2)

Add '-2x2' to each side of the equation.
3 + 5x + 2x2 + -2x2 = -1 + -1x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3 + 5x + 0 = -1 + -1x + 2x2 + -2x2
3 + 5x = -1 + -1x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3 + 5x = -1 + -1x + 0
3 + 5x = -1 + -1x

Solving
3 + 5x = -1 + -1x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add 'x' to each side of the equation.
3 + 5x + x = -1 + -1x + x

Combine like terms: 5x + x = 6x
3 + 6x = -1 + -1x + x

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

Add '-3' to each side of the equation.
3 + -3 + 6x = -1 + -3

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

Combine like terms: -1 + -3 = -4
6x = -4

Divide each side by '6'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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