3x^2+192x-3x-72=0

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Solution for 3x^2+192x-3x-72=0 equation: 


Simplifying
3x2 + 192x + -3x + -72 = 0

Reorder the terms:
-72 + 192x + -3x + 3x2 = 0

Combine like terms: 192x + -3x = 189x
-72 + 189x + 3x2 = 0

Solving
-72 + 189x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 63x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-24 + 63x + x2)' equal to zero and attempt to solve:

Simplifying
-24 + 63x + x2 = 0

Solving
-24 + 63x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 63x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 63x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 63x + x2 = 0 + 24
63x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
63x + x2 = 24

The x term is 63x.  Take half its coefficient (31.5).
Square it (992.25) and add it to both sides.

Add '992.25' to each side of the equation.
63x + 992.25 + x2 = 24 + 992.25

Reorder the terms:
992.25 + 63x + x2 = 24 + 992.25

Combine like terms: 24 + 992.25 = 1016.25
992.25 + 63x + x2 = 1016.25

Factor a perfect square on the left side:
(x + 31.5)(x + 31.5) = 1016.25

Calculate the square root of the right side: 31.878676259

Break this problem into two subproblems by setting 
(x + 31.5) equal to 31.878676259 and -31.878676259.


Subproblem 1
x + 31.5 = 31.878676259

Simplifying
x + 31.5 = 31.878676259

Reorder the terms:
31.5 + x = 31.878676259

Solving
31.5 + x = 31.878676259

Solving for variable 'x'.

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

Add '-31.5' to each side of the equation.
31.5 + -31.5 + x = 31.878676259 + -31.5

Combine like terms: 31.5 + -31.5 = 0.0
0.0 + x = 31.878676259 + -31.5
x = 31.878676259 + -31.5

Combine like terms: 31.878676259 + -31.5 = 0.378676259
x = 0.378676259

Simplifying
x = 0.378676259


Subproblem 2
x + 31.5 = -31.878676259

Simplifying
x + 31.5 = -31.878676259

Reorder the terms:
31.5 + x = -31.878676259

Solving
31.5 + x = -31.878676259

Solving for variable 'x'.

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

Add '-31.5' to each side of the equation.
31.5 + -31.5 + x = -31.878676259 + -31.5

Combine like terms: 31.5 + -31.5 = 0.0
0.0 + x = -31.878676259 + -31.5
x = -31.878676259 + -31.5

Combine like terms: -31.878676259 + -31.5 = -63.378676259
x = -63.378676259

Simplifying
x = -63.378676259


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.378676259, -63.378676259}
Solution
x = {0.378676259, -63.378676259}

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