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

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

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

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

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

Multiply (3 + 4x) * (-2 + x)
(3(-2 + x) + 4x * (-2 + x)) = (x + 3)(x + -1)
((-2 * 3 + x * 3) + 4x * (-2 + x)) = (x + 3)(x + -1)
((-6 + 3x) + 4x * (-2 + x)) = (x + 3)(x + -1)
(-6 + 3x + (-2 * 4x + x * 4x)) = (x + 3)(x + -1)
(-6 + 3x + (-8x + 4x2)) = (x + 3)(x + -1)

Combine like terms: 3x + -8x = -5x
(-6 + -5x + 4x2) = (x + 3)(x + -1)

Reorder the terms:
-6 + -5x + 4x2 = (3 + x)(x + -1)

Reorder the terms:
-6 + -5x + 4x2 = (3 + x)(-1 + x)

Multiply (3 + x) * (-1 + x)
-6 + -5x + 4x2 = (3(-1 + x) + x(-1 + x))
-6 + -5x + 4x2 = ((-1 * 3 + x * 3) + x(-1 + x))
-6 + -5x + 4x2 = ((-3 + 3x) + x(-1 + x))
-6 + -5x + 4x2 = (-3 + 3x + (-1 * x + x * x))
-6 + -5x + 4x2 = (-3 + 3x + (-1x + x2))

Combine like terms: 3x + -1x = 2x
-6 + -5x + 4x2 = (-3 + 2x + x2)

Solving
-6 + -5x + 4x2 = -3 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-6 + 3 + -5x + -2x + 4x2 + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

Combine like terms: -6 + 3 = -3
-3 + -5x + -2x + 4x2 + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

Combine like terms: -5x + -2x = -7x
-3 + -7x + 4x2 + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

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

Reorder the terms:
-3 + -7x + 3x2 = -3 + 3 + 2x + -2x + x2 + -1x2

Combine like terms: -3 + 3 = 0
-3 + -7x + 3x2 = 0 + 2x + -2x + x2 + -1x2
-3 + -7x + 3x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-3 + -7x + 3x2 = 0 + x2 + -1x2
-3 + -7x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + -7x + 3x2 = 0

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

Divide each side by '3'.
-1 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2.333333333x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -2.333333333x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2.333333333x + x2 = 0 + 1
-2.333333333x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2.333333333x + x2 = 1

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 1 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 1 + 1.361111112

Combine like terms: 1 + 1.361111112 = 2.361111112
1.361111112 + -2.333333333x + x2 = 2.361111112

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 2.361111112

Calculate the square root of the right side: 1.536590743

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 1.536590743 and -1.536590743.

Subproblem 1
x + -1.166666667 = 1.536590743

Simplifying
x + -1.166666667 = 1.536590743

Reorder the terms:
-1.166666667 + x = 1.536590743

Solving
-1.166666667 + x = 1.536590743

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 1.536590743 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 1.536590743 + 1.166666667
x = 1.536590743 + 1.166666667

Combine like terms: 1.536590743 + 1.166666667 = 2.70325741
x = 2.70325741

Simplifying
x = 2.70325741

Subproblem 2
x + -1.166666667 = -1.536590743

Simplifying
x + -1.166666667 = -1.536590743

Reorder the terms:
-1.166666667 + x = -1.536590743

Solving
-1.166666667 + x = -1.536590743

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -1.536590743 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -1.536590743 + 1.166666667
x = -1.536590743 + 1.166666667

Combine like terms: -1.536590743 + 1.166666667 = -0.369924076
x = -0.369924076

Simplifying
x = -0.369924076

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.70325741, -0.369924076}