0=6x^2-96x+144

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Solution for 0=6x^2-96x+144 equation: 


Simplifying
0 = 6x2 + -96x + 144

Reorder the terms:
0 = 144 + -96x + 6x2

Solving
0 = 144 + -96x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + -144 = -144
-144 + 96x + -6x2 = 144 + -96x + 6x2 + -144 + 96x + -6x2

Reorder the terms:
-144 + 96x + -6x2 = 144 + -144 + -96x + 96x + 6x2 + -6x2

Combine like terms: 144 + -144 = 0
-144 + 96x + -6x2 = 0 + -96x + 96x + 6x2 + -6x2
-144 + 96x + -6x2 = -96x + 96x + 6x2 + -6x2

Combine like terms: -96x + 96x = 0
-144 + 96x + -6x2 = 0 + 6x2 + -6x2
-144 + 96x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-144 + 96x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-24 + 16x + -1x2) = 0

Ignore the factor 6.

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

Simplifying
-24 + 16x + -1x2 = 0

Solving
-24 + 16x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
24 + -16x + x2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -16x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -16x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -16x + x2 = 0 + -24
-16x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-16x + x2 = -24

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -24 + 64

Reorder the terms:
64 + -16x + x2 = -24 + 64

Combine like terms: -24 + 64 = 40
64 + -16x + x2 = 40

Factor a perfect square on the left side:
(x + -8)(x + -8) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + -8) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + -8 = 6.32455532

Simplifying
x + -8 = 6.32455532

Reorder the terms:
-8 + x = 6.32455532

Solving
-8 + x = 6.32455532

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 6.32455532 + 8

Combine like terms: -8 + 8 = 0
0 + x = 6.32455532 + 8
x = 6.32455532 + 8

Combine like terms: 6.32455532 + 8 = 14.32455532
x = 14.32455532

Simplifying
x = 14.32455532


Subproblem 2
x + -8 = -6.32455532

Simplifying
x + -8 = -6.32455532

Reorder the terms:
-8 + x = -6.32455532

Solving
-8 + x = -6.32455532

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -6.32455532 + 8

Combine like terms: -8 + 8 = 0
0 + x = -6.32455532 + 8
x = -6.32455532 + 8

Combine like terms: -6.32455532 + 8 = 1.67544468
x = 1.67544468

Simplifying
x = 1.67544468


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.32455532, 1.67544468}
Solution
x = {14.32455532, 1.67544468}

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