4(x^2+6x-864)=0

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Solution for 4(x^2+6x-864)=0 equation: 


Simplifying
4(x2 + 6x + -864) = 0

Reorder the terms:
4(-864 + 6x + x2) = 0
(-864 * 4 + 6x * 4 + x2 * 4) = 0
(-3456 + 24x + 4x2) = 0

Solving
-3456 + 24x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-864 + 6x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-864 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-864 + 6x + x2 = 0

Solving
-864 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '864' to each side of the equation.
-864 + 6x + 864 + x2 = 0 + 864

Reorder the terms:
-864 + 864 + 6x + x2 = 0 + 864

Combine like terms: -864 + 864 = 0
0 + 6x + x2 = 0 + 864
6x + x2 = 0 + 864

Combine like terms: 0 + 864 = 864
6x + x2 = 864

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 864 + 9

Reorder the terms:
9 + 6x + x2 = 864 + 9

Combine like terms: 864 + 9 = 873
9 + 6x + x2 = 873

Factor a perfect square on the left side:
(x + 3)(x + 3) = 873

Calculate the square root of the right side: 29.546573405

Break this problem into two subproblems by setting 
(x + 3) equal to 29.546573405 and -29.546573405.


Subproblem 1
x + 3 = 29.546573405

Simplifying
x + 3 = 29.546573405

Reorder the terms:
3 + x = 29.546573405

Solving
3 + x = 29.546573405

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 29.546573405 + -3

Combine like terms: 3 + -3 = 0
0 + x = 29.546573405 + -3
x = 29.546573405 + -3

Combine like terms: 29.546573405 + -3 = 26.546573405
x = 26.546573405

Simplifying
x = 26.546573405


Subproblem 2
x + 3 = -29.546573405

Simplifying
x + 3 = -29.546573405

Reorder the terms:
3 + x = -29.546573405

Solving
3 + x = -29.546573405

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -29.546573405 + -3

Combine like terms: 3 + -3 = 0
0 + x = -29.546573405 + -3
x = -29.546573405 + -3

Combine like terms: -29.546573405 + -3 = -32.546573405
x = -32.546573405

Simplifying
x = -32.546573405


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.546573405, -32.546573405}
Solution
x = {26.546573405, -32.546573405}

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