6x^2-48x+32=0

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Solution for 6x^2-48x+32=0 equation: 


Simplifying
6x2 + -48x + 32 = 0

Reorder the terms:
32 + -48x + 6x2 = 0

Solving
32 + -48x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -24x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + -24x + 3x2)' equal to zero and attempt to solve:

Simplifying
16 + -24x + 3x2 = 0

Solving
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 = 10.666666667
16 + -8x + x2 = 10.666666667

Factor a perfect square on the left side:
(x + -4)(x + -4) = 10.666666667

Calculate the square root of the right side: 3.265986324

Break this problem into two subproblems by setting 
(x + -4) equal to 3.265986324 and -3.265986324.


Subproblem 1
x + -4 = 3.265986324

Simplifying
x + -4 = 3.265986324

Reorder the terms:
-4 + x = 3.265986324

Solving
-4 + x = 3.265986324

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 = 3.265986324 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.265986324 + 4
x = 3.265986324 + 4

Combine like terms: 3.265986324 + 4 = 7.265986324
x = 7.265986324

Simplifying
x = 7.265986324


Subproblem 2
x + -4 = -3.265986324

Simplifying
x + -4 = -3.265986324

Reorder the terms:
-4 + x = -3.265986324

Solving
-4 + x = -3.265986324

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 = -3.265986324 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.265986324 + 4
x = -3.265986324 + 4

Combine like terms: -3.265986324 + 4 = 0.734013676
x = 0.734013676

Simplifying
x = 0.734013676


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.265986324, 0.734013676}
Solution
x = {7.265986324, 0.734013676}

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