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

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

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

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

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

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

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

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

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

Multiply (-3 + 2x) * (4 + x)
-2 + 1x + x2 = (-3(4 + x) + 2x * (4 + x))
-2 + 1x + x2 = ((4 * -3 + x * -3) + 2x * (4 + x))
-2 + 1x + x2 = ((-12 + -3x) + 2x * (4 + x))
-2 + 1x + x2 = (-12 + -3x + (4 * 2x + x * 2x))
-2 + 1x + x2 = (-12 + -3x + (8x + 2x2))

Combine like terms: -3x + 8x = 5x
-2 + 1x + x2 = (-12 + 5x + 2x2)

Solving
-2 + 1x + x2 = -12 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-2 + 12 + 1x + -5x + x2 + -2x2 = -12 + 5x + 2x2 + 12 + -5x + -2x2

Combine like terms: -2 + 12 = 10
10 + 1x + -5x + x2 + -2x2 = -12 + 5x + 2x2 + 12 + -5x + -2x2

Combine like terms: 1x + -5x = -4x
10 + -4x + x2 + -2x2 = -12 + 5x + 2x2 + 12 + -5x + -2x2

Combine like terms: x2 + -2x2 = -1x2
10 + -4x + -1x2 = -12 + 5x + 2x2 + 12 + -5x + -2x2

Reorder the terms:
10 + -4x + -1x2 = -12 + 12 + 5x + -5x + 2x2 + -2x2

Combine like terms: -12 + 12 = 0
10 + -4x + -1x2 = 0 + 5x + -5x + 2x2 + -2x2
10 + -4x + -1x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
10 + -4x + -1x2 = 0 + 2x2 + -2x2
10 + -4x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
10 + -4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-10 + 4x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 4x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 4x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 4x + x2 = 0 + 10
4x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
4x + x2 = 10

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 10 + 4

Reorder the terms:
4 + 4x + x2 = 10 + 4

Combine like terms: 10 + 4 = 14
4 + 4x + x2 = 14

Factor a perfect square on the left side:
(x + 2)(x + 2) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + 2) equal to 3.741657387 and -3.741657387.

Subproblem 1
x + 2 = 3.741657387

Simplifying
x + 2 = 3.741657387

Reorder the terms:
2 + x = 3.741657387

Solving
2 + x = 3.741657387

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 3.741657387 + -2

Combine like terms: 2 + -2 = 0
0 + x = 3.741657387 + -2
x = 3.741657387 + -2

Combine like terms: 3.741657387 + -2 = 1.741657387
x = 1.741657387

Simplifying
x = 1.741657387

Subproblem 2
x + 2 = -3.741657387

Simplifying
x + 2 = -3.741657387

Reorder the terms:
2 + x = -3.741657387

Solving
2 + x = -3.741657387

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -3.741657387 + -2

Combine like terms: 2 + -2 = 0
0 + x = -3.741657387 + -2
x = -3.741657387 + -2

Combine like terms: -3.741657387 + -2 = -5.741657387
x = -5.741657387

Simplifying
x = -5.741657387

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.741657387, -5.741657387}