6x(x+4)=48

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Solution for 6x(x+4)=48 equation: 


Simplifying
6x(x + 4) = 48

Reorder the terms:
6x(4 + x) = 48
(4 * 6x + x * 6x) = 48
(24x + 6x2) = 48

Solving
24x + 6x2 = 48

Solving for variable 'x'.

Reorder the terms:
-48 + 24x + 6x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 24x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-8 + 4x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-8 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-8 + 4x + x2 = 0

Solving
-8 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 4x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 4x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 4x + x2 = 0 + 8
4x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
4x + x2 = 8

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 = 8 + 4

Reorder the terms:
4 + 4x + x2 = 8 + 4

Combine like terms: 8 + 4 = 12
4 + 4x + x2 = 12

Factor a perfect square on the left side:
(x + 2)(x + 2) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + 2) equal to 3.464101615 and -3.464101615.


Subproblem 1
x + 2 = 3.464101615

Simplifying
x + 2 = 3.464101615

Reorder the terms:
2 + x = 3.464101615

Solving
2 + x = 3.464101615

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 = 3.464101615 + -2

Combine like terms: 2 + -2 = 0
0 + x = 3.464101615 + -2
x = 3.464101615 + -2

Combine like terms: 3.464101615 + -2 = 1.464101615
x = 1.464101615

Simplifying
x = 1.464101615


Subproblem 2
x + 2 = -3.464101615

Simplifying
x + 2 = -3.464101615

Reorder the terms:
2 + x = -3.464101615

Solving
2 + x = -3.464101615

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 = -3.464101615 + -2

Combine like terms: 2 + -2 = 0
0 + x = -3.464101615 + -2
x = -3.464101615 + -2

Combine like terms: -3.464101615 + -2 = -5.464101615
x = -5.464101615

Simplifying
x = -5.464101615


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.464101615, -5.464101615}
Solution
x = {1.464101615, -5.464101615}

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