12(405-48x+x^2)=0

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Solution for 12(405-48x+x^2)=0 equation: 


Simplifying
12(405 + -48x + x2) = 0
(405 * 12 + -48x * 12 + x2 * 12) = 0
(4860 + -576x + 12x2) = 0

Solving
4860 + -576x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(405 + -48x + x2) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(405 + -48x + x2)' equal to zero and attempt to solve:

Simplifying
405 + -48x + x2 = 0

Solving
405 + -48x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-405' to each side of the equation.
405 + -48x + -405 + x2 = 0 + -405

Reorder the terms:
405 + -405 + -48x + x2 = 0 + -405

Combine like terms: 405 + -405 = 0
0 + -48x + x2 = 0 + -405
-48x + x2 = 0 + -405

Combine like terms: 0 + -405 = -405
-48x + x2 = -405

The x term is -48x.  Take half its coefficient (-24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
-48x + 576 + x2 = -405 + 576

Reorder the terms:
576 + -48x + x2 = -405 + 576

Combine like terms: -405 + 576 = 171
576 + -48x + x2 = 171

Factor a perfect square on the left side:
(x + -24)(x + -24) = 171

Calculate the square root of the right side: 13.076696831

Break this problem into two subproblems by setting 
(x + -24) equal to 13.076696831 and -13.076696831.


Subproblem 1
x + -24 = 13.076696831

Simplifying
x + -24 = 13.076696831

Reorder the terms:
-24 + x = 13.076696831

Solving
-24 + x = 13.076696831

Solving for variable 'x'.

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

Add '24' to each side of the equation.
-24 + 24 + x = 13.076696831 + 24

Combine like terms: -24 + 24 = 0
0 + x = 13.076696831 + 24
x = 13.076696831 + 24

Combine like terms: 13.076696831 + 24 = 37.076696831
x = 37.076696831

Simplifying
x = 37.076696831


Subproblem 2
x + -24 = -13.076696831

Simplifying
x + -24 = -13.076696831

Reorder the terms:
-24 + x = -13.076696831

Solving
-24 + x = -13.076696831

Solving for variable 'x'.

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

Add '24' to each side of the equation.
-24 + 24 + x = -13.076696831 + 24

Combine like terms: -24 + 24 = 0
0 + x = -13.076696831 + 24
x = -13.076696831 + 24

Combine like terms: -13.076696831 + 24 = 10.923303169
x = 10.923303169

Simplifying
x = 10.923303169


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {37.076696831, 10.923303169}
Solution
x = {37.076696831, 10.923303169}

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