3x(x+8)=16

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Solution for 3x(x+8)=16 equation: 


Simplifying
3x(x + 8) = 16

Reorder the terms:
3x(8 + x) = 16
(8 * 3x + x * 3x) = 16
(24x + 3x2) = 16

Solving
24x + 3x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + 24x + 3x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 24x + 3x2 = 0

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

Divide each side by '3'.
-5.333333333 + 8x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + 8x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + 8x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + 8x + x2 = 0 + 5.333333333
8x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
8x + x2 = 5.333333333

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 5.333333333 + 16

Reorder the terms:
16 + 8x + x2 = 5.333333333 + 16

Combine like terms: 5.333333333 + 16 = 21.333333333
16 + 8x + x2 = 21.333333333

Factor a perfect square on the left side:
(x + 4)(x + 4) = 21.333333333

Calculate the square root of the right side: 4.618802153

Break this problem into two subproblems by setting 
(x + 4) equal to 4.618802153 and -4.618802153.


Subproblem 1
x + 4 = 4.618802153

Simplifying
x + 4 = 4.618802153

Reorder the terms:
4 + x = 4.618802153

Solving
4 + x = 4.618802153

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 4.618802153 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.618802153 + -4
x = 4.618802153 + -4

Combine like terms: 4.618802153 + -4 = 0.618802153
x = 0.618802153

Simplifying
x = 0.618802153


Subproblem 2
x + 4 = -4.618802153

Simplifying
x + 4 = -4.618802153

Reorder the terms:
4 + x = -4.618802153

Solving
4 + x = -4.618802153

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -4.618802153 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.618802153 + -4
x = -4.618802153 + -4

Combine like terms: -4.618802153 + -4 = -8.618802153
x = -8.618802153

Simplifying
x = -8.618802153


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.618802153, -8.618802153}

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