(3x+8)=(x+4)(3x-7)

Solution for (3x+8)=(x+4)(3x-7) equation:

Simplifying
(3x + 8) = (x + 4)(3x + -7)

Reorder the terms:
(8 + 3x) = (x + 4)(3x + -7)

Remove parenthesis around (8 + 3x)
8 + 3x = (x + 4)(3x + -7)

Reorder the terms:
8 + 3x = (4 + x)(3x + -7)

Reorder the terms:
8 + 3x = (4 + x)(-7 + 3x)

Multiply (4 + x) * (-7 + 3x)
8 + 3x = (4(-7 + 3x) + x(-7 + 3x))
8 + 3x = ((-7 * 4 + 3x * 4) + x(-7 + 3x))
8 + 3x = ((-28 + 12x) + x(-7 + 3x))
8 + 3x = (-28 + 12x + (-7 * x + 3x * x))
8 + 3x = (-28 + 12x + (-7x + 3x2))

Combine like terms: 12x + -7x = 5x
8 + 3x = (-28 + 5x + 3x2)

Solving
8 + 3x = -28 + 5x + 3x2

Solving for variable 'x'.

Reorder the terms:
8 + 28 + 3x + -5x + -3x2 = -28 + 5x + 3x2 + 28 + -5x + -3x2

Combine like terms: 8 + 28 = 36
36 + 3x + -5x + -3x2 = -28 + 5x + 3x2 + 28 + -5x + -3x2

Combine like terms: 3x + -5x = -2x
36 + -2x + -3x2 = -28 + 5x + 3x2 + 28 + -5x + -3x2

Reorder the terms:
36 + -2x + -3x2 = -28 + 28 + 5x + -5x + 3x2 + -3x2

Combine like terms: -28 + 28 = 0
36 + -2x + -3x2 = 0 + 5x + -5x + 3x2 + -3x2
36 + -2x + -3x2 = 5x + -5x + 3x2 + -3x2

Combine like terms: 5x + -5x = 0
36 + -2x + -3x2 = 0 + 3x2 + -3x2
36 + -2x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
36 + -2x + -3x2 = 0

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

Divide each side by '-3'.
-12 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 0.6666666667x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 0.6666666667x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 0.6666666667x + x2 = 0 + 12
0.6666666667x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
0.6666666667x + x2 = 12

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 12 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 12 + 0.1111111112

Combine like terms: 12 + 0.1111111112 = 12.1111111112
0.1111111112 + 0.6666666667x + x2 = 12.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 12.1111111112

Calculate the square root of the right side: 3.48010217

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 3.48010217 and -3.48010217.

Subproblem 1
x + 0.3333333334 = 3.48010217

Simplifying
x + 0.3333333334 = 3.48010217

Reorder the terms:
0.3333333334 + x = 3.48010217

Solving
0.3333333334 + x = 3.48010217

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 3.48010217 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 3.48010217 + -0.3333333334
x = 3.48010217 + -0.3333333334

Combine like terms: 3.48010217 + -0.3333333334 = 3.1467688366
x = 3.1467688366

Simplifying
x = 3.1467688366

Subproblem 2
x + 0.3333333334 = -3.48010217

Simplifying
x + 0.3333333334 = -3.48010217

Reorder the terms:
0.3333333334 + x = -3.48010217

Solving
0.3333333334 + x = -3.48010217

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -3.48010217 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -3.48010217 + -0.3333333334
x = -3.48010217 + -0.3333333334

Combine like terms: -3.48010217 + -0.3333333334 = -3.8134355034
x = -3.8134355034

Simplifying
x = -3.8134355034

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.1467688366, -3.8134355034}