3(x+4)21x=72

Solution for 3(x+4)21x=72 equation:

Simplifying
3(x + 4) * 21x = 72

Reorder the terms:
3(4 + x) * 21x = 72

Reorder the terms for easier multiplication:
3 * 21x(4 + x) = 72

Multiply 3 * 21
63x(4 + x) = 72
(4 * 63x + x * 63x) = 72
(252x + 63x2) = 72

Solving
252x + 63x2 = 72

Solving for variable 'x'.

Reorder the terms:
-72 + 252x + 63x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 252x + 63x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-8 + 28x + 7x2) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-8 + 28x + 7x2)' equal to zero and attempt to solve:

Simplifying
-8 + 28x + 7x2 = 0

Solving
-8 + 28x + 7x2 = 0

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

Divide each side by '7'.
-1.142857143 + 4x + x2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + 4x + 1.142857143 + x2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + 4x + x2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + 4x + x2 = 0 + 1.142857143
4x + x2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
4x + x2 = 1.142857143

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 1.142857143 + 4

Reorder the terms:
4 + 4x + x2 = 1.142857143 + 4

Combine like terms: 1.142857143 + 4 = 5.142857143
4 + 4x + x2 = 5.142857143

Factor a perfect square on the left side:
(x + 2)(x + 2) = 5.142857143

Calculate the square root of the right side: 2.267786838

Break this problem into two subproblems by setting 
(x + 2) equal to 2.267786838 and -2.267786838.

Subproblem 1
x + 2 = 2.267786838

Simplifying
x + 2 = 2.267786838

Reorder the terms:
2 + x = 2.267786838

Solving
2 + x = 2.267786838

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.267786838 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.267786838 + -2
x = 2.267786838 + -2

Combine like terms: 2.267786838 + -2 = 0.267786838
x = 0.267786838

Simplifying
x = 0.267786838

Subproblem 2
x + 2 = -2.267786838

Simplifying
x + 2 = -2.267786838

Reorder the terms:
2 + x = -2.267786838

Solving
2 + x = -2.267786838

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.267786838 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.267786838 + -2
x = -2.267786838 + -2

Combine like terms: -2.267786838 + -2 = -4.267786838
x = -4.267786838

Simplifying
x = -4.267786838

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.267786838, -4.267786838}
Solution
x = {0.267786838, -4.267786838}