x(x+4)3=4(x+19.5)

Solution for x(x+4)3=4(x+19.5) equation:

Simplifying
x(x + 4) * 3 = 4(x + 19.5)

Reorder the terms:
x(4 + x) * 3 = 4(x + 19.5)

Reorder the terms for easier multiplication:
3x(4 + x) = 4(x + 19.5)
(4 * 3x + x * 3x) = 4(x + 19.5)
(12x + 3x2) = 4(x + 19.5)

Reorder the terms:
12x + 3x2 = 4(19.5 + x)
12x + 3x2 = (19.5 * 4 + x * 4)
12x + 3x2 = (78 + 4x)

Solving
12x + 3x2 = 78 + 4x

Solving for variable 'x'.

Reorder the terms:
-78 + 12x + -4x + 3x2 = 78 + 4x + -78 + -4x

Combine like terms: 12x + -4x = 8x
-78 + 8x + 3x2 = 78 + 4x + -78 + -4x

Reorder the terms:
-78 + 8x + 3x2 = 78 + -78 + 4x + -4x

Combine like terms: 78 + -78 = 0
-78 + 8x + 3x2 = 0 + 4x + -4x
-78 + 8x + 3x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-78 + 8x + 3x2 = 0

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

Divide each side by '3'.
-26 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 2.666666667x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + 2.666666667x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 2.666666667x + x2 = 0 + 26
2.666666667x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
2.666666667x + x2 = 26

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 26 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 26 + 1.777777780

Combine like terms: 26 + 1.777777780 = 27.77777778
1.777777780 + 2.666666667x + x2 = 27.77777778

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 27.77777778

Calculate the square root of the right side: 5.270462767

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 5.270462767 and -5.270462767.

Subproblem 1
x + 1.333333334 = 5.270462767

Simplifying
x + 1.333333334 = 5.270462767

Reorder the terms:
1.333333334 + x = 5.270462767

Solving
1.333333334 + x = 5.270462767

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = 5.270462767 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 5.270462767 + -1.333333334
x = 5.270462767 + -1.333333334

Combine like terms: 5.270462767 + -1.333333334 = 3.937129433
x = 3.937129433

Simplifying
x = 3.937129433

Subproblem 2
x + 1.333333334 = -5.270462767

Simplifying
x + 1.333333334 = -5.270462767

Reorder the terms:
1.333333334 + x = -5.270462767

Solving
1.333333334 + x = -5.270462767

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = -5.270462767 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -5.270462767 + -1.333333334
x = -5.270462767 + -1.333333334

Combine like terms: -5.270462767 + -1.333333334 = -6.603796101
x = -6.603796101

Simplifying
x = -6.603796101

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.937129433, -6.603796101}