(x-8)(2x+3)=(3x-5)(x+4)

Solution for (x-8)(2x+3)=(3x-5)(x+4) equation:

Simplifying
(x + -8)(2x + 3) = (3x + -5)(x + 4)

Reorder the terms:
(-8 + x)(2x + 3) = (3x + -5)(x + 4)

Reorder the terms:
(-8 + x)(3 + 2x) = (3x + -5)(x + 4)

Multiply (-8 + x) * (3 + 2x)
(-8(3 + 2x) + x(3 + 2x)) = (3x + -5)(x + 4)
((3 * -8 + 2x * -8) + x(3 + 2x)) = (3x + -5)(x + 4)
((-24 + -16x) + x(3 + 2x)) = (3x + -5)(x + 4)
(-24 + -16x + (3 * x + 2x * x)) = (3x + -5)(x + 4)
(-24 + -16x + (3x + 2x2)) = (3x + -5)(x + 4)

Combine like terms: -16x + 3x = -13x
(-24 + -13x + 2x2) = (3x + -5)(x + 4)

Reorder the terms:
-24 + -13x + 2x2 = (-5 + 3x)(x + 4)

Reorder the terms:
-24 + -13x + 2x2 = (-5 + 3x)(4 + x)

Multiply (-5 + 3x) * (4 + x)
-24 + -13x + 2x2 = (-5(4 + x) + 3x * (4 + x))
-24 + -13x + 2x2 = ((4 * -5 + x * -5) + 3x * (4 + x))
-24 + -13x + 2x2 = ((-20 + -5x) + 3x * (4 + x))
-24 + -13x + 2x2 = (-20 + -5x + (4 * 3x + x * 3x))
-24 + -13x + 2x2 = (-20 + -5x + (12x + 3x2))

Combine like terms: -5x + 12x = 7x
-24 + -13x + 2x2 = (-20 + 7x + 3x2)

Solving
-24 + -13x + 2x2 = -20 + 7x + 3x2

Solving for variable 'x'.

Reorder the terms:
-24 + 20 + -13x + -7x + 2x2 + -3x2 = -20 + 7x + 3x2 + 20 + -7x + -3x2

Combine like terms: -24 + 20 = -4
-4 + -13x + -7x + 2x2 + -3x2 = -20 + 7x + 3x2 + 20 + -7x + -3x2

Combine like terms: -13x + -7x = -20x
-4 + -20x + 2x2 + -3x2 = -20 + 7x + 3x2 + 20 + -7x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
-4 + -20x + -1x2 = -20 + 7x + 3x2 + 20 + -7x + -3x2

Reorder the terms:
-4 + -20x + -1x2 = -20 + 20 + 7x + -7x + 3x2 + -3x2

Combine like terms: -20 + 20 = 0
-4 + -20x + -1x2 = 0 + 7x + -7x + 3x2 + -3x2
-4 + -20x + -1x2 = 7x + -7x + 3x2 + -3x2

Combine like terms: 7x + -7x = 0
-4 + -20x + -1x2 = 0 + 3x2 + -3x2
-4 + -20x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-4 + -20x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 20x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(4 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
4 + 20x + x2 = 0

Solving
4 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 20x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 20x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 20x + x2 = 0 + -4
20x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
20x + x2 = -4

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -4 + 100

Reorder the terms:
100 + 20x + x2 = -4 + 100

Combine like terms: -4 + 100 = 96
100 + 20x + x2 = 96

Factor a perfect square on the left side:
(x + 10)(x + 10) = 96

Calculate the square root of the right side: 9.797958971

Break this problem into two subproblems by setting 
(x + 10) equal to 9.797958971 and -9.797958971.

Subproblem 1
x + 10 = 9.797958971

Simplifying
x + 10 = 9.797958971

Reorder the terms:
10 + x = 9.797958971

Solving
10 + x = 9.797958971

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 9.797958971 + -10

Combine like terms: 10 + -10 = 0
0 + x = 9.797958971 + -10
x = 9.797958971 + -10

Combine like terms: 9.797958971 + -10 = -0.202041029
x = -0.202041029

Simplifying
x = -0.202041029

Subproblem 2
x + 10 = -9.797958971

Simplifying
x + 10 = -9.797958971

Reorder the terms:
10 + x = -9.797958971

Solving
10 + x = -9.797958971

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -9.797958971 + -10

Combine like terms: 10 + -10 = 0
0 + x = -9.797958971 + -10
x = -9.797958971 + -10

Combine like terms: -9.797958971 + -10 = -19.797958971
x = -19.797958971

Simplifying
x = -19.797958971

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.202041029, -19.797958971}
Solution
x = {-0.202041029, -19.797958971}