(8x+432)(x+6)=576

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Solution for (8x+432)(x+6)=576 equation: 


Simplifying
(8x + 432)(x + 6) = 576

Reorder the terms:
(432 + 8x)(x + 6) = 576

Reorder the terms:
(432 + 8x)(6 + x) = 576

Multiply (432 + 8x) * (6 + x)
(432(6 + x) + 8x * (6 + x)) = 576
((6 * 432 + x * 432) + 8x * (6 + x)) = 576
((2592 + 432x) + 8x * (6 + x)) = 576
(2592 + 432x + (6 * 8x + x * 8x)) = 576
(2592 + 432x + (48x + 8x2)) = 576

Combine like terms: 432x + 48x = 480x
(2592 + 480x + 8x2) = 576

Solving
2592 + 480x + 8x2 = 576

Solving for variable 'x'.

Reorder the terms:
2592 + -576 + 480x + 8x2 = 576 + -576

Combine like terms: 2592 + -576 = 2016
2016 + 480x + 8x2 = 576 + -576

Combine like terms: 576 + -576 = 0
2016 + 480x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(252 + 60x + x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(252 + 60x + x2)' equal to zero and attempt to solve:

Simplifying
252 + 60x + x2 = 0

Solving
252 + 60x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-252' to each side of the equation.
252 + 60x + -252 + x2 = 0 + -252

Reorder the terms:
252 + -252 + 60x + x2 = 0 + -252

Combine like terms: 252 + -252 = 0
0 + 60x + x2 = 0 + -252
60x + x2 = 0 + -252

Combine like terms: 0 + -252 = -252
60x + x2 = -252

The x term is 60x.  Take half its coefficient (30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
60x + 900 + x2 = -252 + 900

Reorder the terms:
900 + 60x + x2 = -252 + 900

Combine like terms: -252 + 900 = 648
900 + 60x + x2 = 648

Factor a perfect square on the left side:
(x + 30)(x + 30) = 648

Calculate the square root of the right side: 25.455844123

Break this problem into two subproblems by setting 
(x + 30) equal to 25.455844123 and -25.455844123.


Subproblem 1
x + 30 = 25.455844123

Simplifying
x + 30 = 25.455844123

Reorder the terms:
30 + x = 25.455844123

Solving
30 + x = 25.455844123

Solving for variable 'x'.

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

Add '-30' to each side of the equation.
30 + -30 + x = 25.455844123 + -30

Combine like terms: 30 + -30 = 0
0 + x = 25.455844123 + -30
x = 25.455844123 + -30

Combine like terms: 25.455844123 + -30 = -4.544155877
x = -4.544155877

Simplifying
x = -4.544155877


Subproblem 2
x + 30 = -25.455844123

Simplifying
x + 30 = -25.455844123

Reorder the terms:
30 + x = -25.455844123

Solving
30 + x = -25.455844123

Solving for variable 'x'.

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

Add '-30' to each side of the equation.
30 + -30 + x = -25.455844123 + -30

Combine like terms: 30 + -30 = 0
0 + x = -25.455844123 + -30
x = -25.455844123 + -30

Combine like terms: -25.455844123 + -30 = -55.455844123
x = -55.455844123

Simplifying
x = -55.455844123


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.544155877, -55.455844123}
Solution
x = {-4.544155877, -55.455844123}

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