2(3x^2-4x-48)=0

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Solution for 2(3x^2-4x-48)=0 equation: 


Simplifying
2(3x2 + -4x + -48) = 0

Reorder the terms:
2(-48 + -4x + 3x2) = 0
(-48 * 2 + -4x * 2 + 3x2 * 2) = 0
(-96 + -8x + 6x2) = 0

Solving
-96 + -8x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + -4x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-48 + -4x + 3x2)' equal to zero and attempt to solve:

Simplifying
-48 + -4x + 3x2 = 0

Solving
-48 + -4x + 3x2 = 0

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

Divide each side by '3'.
-16 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -1.333333333x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -1.333333333x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1.333333333x + x2 = 0 + 16
-1.333333333x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-1.333333333x + x2 = 16

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 16 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 16 + 0.4444444442

Combine like terms: 16 + 0.4444444442 = 16.4444444442
0.4444444442 + -1.333333333x + x2 = 16.4444444442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 16.4444444442

Calculate the square root of the right side: 4.05517502

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 4.05517502 and -4.05517502.


Subproblem 1
x + -0.6666666665 = 4.05517502

Simplifying
x + -0.6666666665 = 4.05517502

Reorder the terms:
-0.6666666665 + x = 4.05517502

Solving
-0.6666666665 + x = 4.05517502

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 4.05517502 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 4.05517502 + 0.6666666665
x = 4.05517502 + 0.6666666665

Combine like terms: 4.05517502 + 0.6666666665 = 4.7218416865
x = 4.7218416865

Simplifying
x = 4.7218416865


Subproblem 2
x + -0.6666666665 = -4.05517502

Simplifying
x + -0.6666666665 = -4.05517502

Reorder the terms:
-0.6666666665 + x = -4.05517502

Solving
-0.6666666665 + x = -4.05517502

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -4.05517502 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -4.05517502 + 0.6666666665
x = -4.05517502 + 0.6666666665

Combine like terms: -4.05517502 + 0.6666666665 = -3.3885083535
x = -3.3885083535

Simplifying
x = -3.3885083535


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.7218416865, -3.3885083535}
Solution
x = {4.7218416865, -3.3885083535}

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