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

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

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

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

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

Multiply (-3 + 2x) * (-2 + x)
(-3(-2 + x) + 2x * (-2 + x)) + 2x = x + 1
((-2 * -3 + x * -3) + 2x * (-2 + x)) + 2x = x + 1
((6 + -3x) + 2x * (-2 + x)) + 2x = x + 1
(6 + -3x + (-2 * 2x + x * 2x)) + 2x = x + 1
(6 + -3x + (-4x + 2x2)) + 2x = x + 1

Combine like terms: -3x + -4x = -7x
(6 + -7x + 2x2) + 2x = x + 1

Reorder the terms:
6 + -7x + 2x + 2x2 = x + 1

Combine like terms: -7x + 2x = -5x
6 + -5x + 2x2 = x + 1

Reorder the terms:
6 + -5x + 2x2 = 1 + x

Solving
6 + -5x + 2x2 = 1 + x

Solving for variable 'x'.

Reorder the terms:
6 + -1 + -5x + -1x + 2x2 = 1 + x + -1 + -1x

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

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

Reorder the terms:
5 + -6x + 2x2 = 1 + -1 + x + -1x

Combine like terms: 1 + -1 = 0
5 + -6x + 2x2 = 0 + x + -1x
5 + -6x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
5 + -6x + 2x2 = 0

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

Divide each side by '2'.
2.5 + -3x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -3x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -3x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -3x + x2 = 0 + -2.5
-3x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-3x + x2 = -2.5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -2.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -2.5 + 2.25

Combine like terms: -2.5 + 2.25 = -0.25
2.25 + -3x + x2 = -0.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.