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

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

Simplifying
(2x + 1)(x + 4) = 3(x2 + -4)

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

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

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

Combine like terms: 1x + 8x = 9x
(4 + 9x + 2x2) = 3(x2 + -4)

Reorder the terms:
4 + 9x + 2x2 = 3(-4 + x2)
4 + 9x + 2x2 = (-4 * 3 + x2 * 3)
4 + 9x + 2x2 = (-12 + 3x2)

Solving
4 + 9x + 2x2 = -12 + 3x2

Solving for variable 'x'.

Reorder the terms:
4 + 12 + 9x + 2x2 + -3x2 = -12 + 3x2 + 12 + -3x2

Combine like terms: 4 + 12 = 16
16 + 9x + 2x2 + -3x2 = -12 + 3x2 + 12 + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
16 + 9x + -1x2 = -12 + 3x2 + 12 + -3x2

Reorder the terms:
16 + 9x + -1x2 = -12 + 12 + 3x2 + -3x2

Combine like terms: -12 + 12 = 0
16 + 9x + -1x2 = 0 + 3x2 + -3x2
16 + 9x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
16 + 9x + -1x2 = 0

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

Divide each side by '-1'.
-16 + -9x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -9x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -9x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -9x + x2 = 0 + 16
-9x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-9x + x2 = 16

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 16 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 16 + 20.25

Combine like terms: 16 + 20.25 = 36.25
20.25 + -9x + x2 = 36.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x + -4.5) equal to 6.020797289 and -6.020797289.

Subproblem 1
x + -4.5 = 6.020797289

Simplifying
x + -4.5 = 6.020797289

Reorder the terms:
-4.5 + x = 6.020797289

Solving
-4.5 + x = 6.020797289

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 6.020797289 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 6.020797289 + 4.5
x = 6.020797289 + 4.5

Combine like terms: 6.020797289 + 4.5 = 10.520797289
x = 10.520797289

Simplifying
x = 10.520797289

Subproblem 2
x + -4.5 = -6.020797289

Simplifying
x + -4.5 = -6.020797289

Reorder the terms:
-4.5 + x = -6.020797289

Solving
-4.5 + x = -6.020797289

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -6.020797289 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -6.020797289 + 4.5
x = -6.020797289 + 4.5

Combine like terms: -6.020797289 + 4.5 = -1.520797289
x = -1.520797289

Simplifying
x = -1.520797289

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.520797289, -1.520797289}