(4x+3)(x-2)=(x+6)(3x+4)

Solution for (4x+3)(x-2)=(x+6)(3x+4) equation:

Simplifying
(4x + 3)(x + -2) = (x + 6)(3x + 4)

Reorder the terms:
(3 + 4x)(x + -2) = (x + 6)(3x + 4)

Reorder the terms:
(3 + 4x)(-2 + x) = (x + 6)(3x + 4)

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

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

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

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

Multiply (6 + x) * (4 + 3x)
-6 + -5x + 4x2 = (6(4 + 3x) + x(4 + 3x))
-6 + -5x + 4x2 = ((4 * 6 + 3x * 6) + x(4 + 3x))
-6 + -5x + 4x2 = ((24 + 18x) + x(4 + 3x))
-6 + -5x + 4x2 = (24 + 18x + (4 * x + 3x * x))
-6 + -5x + 4x2 = (24 + 18x + (4x + 3x2))

Combine like terms: 18x + 4x = 22x
-6 + -5x + 4x2 = (24 + 22x + 3x2)

Solving
-6 + -5x + 4x2 = 24 + 22x + 3x2

Solving for variable 'x'.

Reorder the terms:
-6 + -24 + -5x + -22x + 4x2 + -3x2 = 24 + 22x + 3x2 + -24 + -22x + -3x2

Combine like terms: -6 + -24 = -30
-30 + -5x + -22x + 4x2 + -3x2 = 24 + 22x + 3x2 + -24 + -22x + -3x2

Combine like terms: -5x + -22x = -27x
-30 + -27x + 4x2 + -3x2 = 24 + 22x + 3x2 + -24 + -22x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
-30 + -27x + 1x2 = 24 + 22x + 3x2 + -24 + -22x + -3x2

Reorder the terms:
-30 + -27x + 1x2 = 24 + -24 + 22x + -22x + 3x2 + -3x2

Combine like terms: 24 + -24 = 0
-30 + -27x + 1x2 = 0 + 22x + -22x + 3x2 + -3x2
-30 + -27x + 1x2 = 22x + -22x + 3x2 + -3x2

Combine like terms: 22x + -22x = 0
-30 + -27x + 1x2 = 0 + 3x2 + -3x2
-30 + -27x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-30 + -27x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -27x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -27x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -27x + x2 = 0 + 30
-27x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-27x + x2 = 30

The x term is -27x.  Take half its coefficient (-13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
-27x + 182.25 + x2 = 30 + 182.25

Reorder the terms:
182.25 + -27x + x2 = 30 + 182.25

Combine like terms: 30 + 182.25 = 212.25
182.25 + -27x + x2 = 212.25

Factor a perfect square on the left side:
(x + -13.5)(x + -13.5) = 212.25

Calculate the square root of the right side: 14.568802284

Break this problem into two subproblems by setting 
(x + -13.5) equal to 14.568802284 and -14.568802284.

Subproblem 1
x + -13.5 = 14.568802284

Simplifying
x + -13.5 = 14.568802284

Reorder the terms:
-13.5 + x = 14.568802284

Solving
-13.5 + x = 14.568802284

Solving for variable 'x'.

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

Add '13.5' to each side of the equation.
-13.5 + 13.5 + x = 14.568802284 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + x = 14.568802284 + 13.5
x = 14.568802284 + 13.5

Combine like terms: 14.568802284 + 13.5 = 28.068802284
x = 28.068802284

Simplifying
x = 28.068802284

Subproblem 2
x + -13.5 = -14.568802284

Simplifying
x + -13.5 = -14.568802284

Reorder the terms:
-13.5 + x = -14.568802284

Solving
-13.5 + x = -14.568802284

Solving for variable 'x'.

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

Add '13.5' to each side of the equation.
-13.5 + 13.5 + x = -14.568802284 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + x = -14.568802284 + 13.5
x = -14.568802284 + 13.5

Combine like terms: -14.568802284 + 13.5 = -1.068802284
x = -1.068802284

Simplifying
x = -1.068802284

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.068802284, -1.068802284}