3x(x+8)=24

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Solution for 3x(x+8)=24 equation: 


Simplifying
3x(x + 8) = 24

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

Solving
24x + 3x2 = 24

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 8x + x2) = 0

Ignore the factor 3.

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

Simplifying
-8 + 8x + x2 = 0

Solving
-8 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 8 + 16

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

Combine like terms: 8 + 16 = 24
16 + 8x + x2 = 24

Factor a perfect square on the left side:
(x + 4)(x + 4) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + 4) equal to 4.898979486 and -4.898979486.


Subproblem 1
x + 4 = 4.898979486

Simplifying
x + 4 = 4.898979486

Reorder the terms:
4 + x = 4.898979486

Solving
4 + x = 4.898979486

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 = 4.898979486 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.898979486 + -4
x = 4.898979486 + -4

Combine like terms: 4.898979486 + -4 = 0.898979486
x = 0.898979486

Simplifying
x = 0.898979486


Subproblem 2
x + 4 = -4.898979486

Simplifying
x + 4 = -4.898979486

Reorder the terms:
4 + x = -4.898979486

Solving
4 + x = -4.898979486

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 = -4.898979486 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.898979486 + -4
x = -4.898979486 + -4

Combine like terms: -4.898979486 + -4 = -8.898979486
x = -8.898979486

Simplifying
x = -8.898979486


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.898979486, -8.898979486}
Solution
x = {0.898979486, -8.898979486}

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