3(x+4)x=7

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


Simplifying
3(x + 4) * x = 7

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

Reorder the terms for easier multiplication:
3x(4 + x) = 7
(4 * 3x + x * 3x) = 7
(12x + 3x2) = 7

Solving
12x + 3x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + 12x + 3x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 12x + 3x2 = 0

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

Divide each side by '3'.
-2.333333333 + 4x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 4x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 4x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 4x + x2 = 0 + 2.333333333
4x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
4x + x2 = 2.333333333

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 = 2.333333333 + 4

Reorder the terms:
4 + 4x + x2 = 2.333333333 + 4

Combine like terms: 2.333333333 + 4 = 6.333333333
4 + 4x + x2 = 6.333333333

Factor a perfect square on the left side:
(x + 2)(x + 2) = 6.333333333

Calculate the square root of the right side: 2.516611478

Break this problem into two subproblems by setting 
(x + 2) equal to 2.516611478 and -2.516611478.


Subproblem 1
x + 2 = 2.516611478

Simplifying
x + 2 = 2.516611478

Reorder the terms:
2 + x = 2.516611478

Solving
2 + x = 2.516611478

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 = 2.516611478 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.516611478 + -2
x = 2.516611478 + -2

Combine like terms: 2.516611478 + -2 = 0.516611478
x = 0.516611478

Simplifying
x = 0.516611478


Subproblem 2
x + 2 = -2.516611478

Simplifying
x + 2 = -2.516611478

Reorder the terms:
2 + x = -2.516611478

Solving
2 + x = -2.516611478

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 = -2.516611478 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.516611478 + -2
x = -2.516611478 + -2

Combine like terms: -2.516611478 + -2 = -4.516611478
x = -4.516611478

Simplifying
x = -4.516611478


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.516611478, -4.516611478}

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