3x(6+x)=24

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Solution for 3x(6+x)=24 equation: 


Simplifying
3x(6 + x) = 24
(6 * 3x + x * 3x) = 24
(18x + 3x2) = 24

Solving
18x + 3x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 18x + 3x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 18x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 6x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-8 + 6x + x2 = 0

Solving
-8 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 6x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 6x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 6x + x2 = 0 + 8
6x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
6x + x2 = 8

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 8 + 9

Reorder the terms:
9 + 6x + x2 = 8 + 9

Combine like terms: 8 + 9 = 17
9 + 6x + x2 = 17

Factor a perfect square on the left side:
(x + 3)(x + 3) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + 3) equal to 4.123105626 and -4.123105626.


Subproblem 1
x + 3 = 4.123105626

Simplifying
x + 3 = 4.123105626

Reorder the terms:
3 + x = 4.123105626

Solving
3 + x = 4.123105626

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 4.123105626 + -3

Combine like terms: 3 + -3 = 0
0 + x = 4.123105626 + -3
x = 4.123105626 + -3

Combine like terms: 4.123105626 + -3 = 1.123105626
x = 1.123105626

Simplifying
x = 1.123105626


Subproblem 2
x + 3 = -4.123105626

Simplifying
x + 3 = -4.123105626

Reorder the terms:
3 + x = -4.123105626

Solving
3 + x = -4.123105626

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -4.123105626 + -3

Combine like terms: 3 + -3 = 0
0 + x = -4.123105626 + -3
x = -4.123105626 + -3

Combine like terms: -4.123105626 + -3 = -7.123105626
x = -7.123105626

Simplifying
x = -7.123105626


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.123105626, -7.123105626}
Solution
x = {1.123105626, -7.123105626}

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