3x^2+-24x+-120=0

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Solution for 3x^2+-24x+-120=0 equation: 


Simplifying
3x2 + -24x + -120 = 0

Reorder the terms:
-120 + -24x + 3x2 = 0

Solving
-120 + -24x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-40 + -8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-40 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-40 + -8x + x2 = 0

Solving
-40 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -8x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -8x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -8x + x2 = 0 + 40
-8x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-8x + x2 = 40

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 40 + 16

Reorder the terms:
16 + -8x + x2 = 40 + 16

Combine like terms: 40 + 16 = 56
16 + -8x + x2 = 56

Factor a perfect square on the left side:
(x + -4)(x + -4) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(x + -4) equal to 7.483314774 and -7.483314774.


Subproblem 1
x + -4 = 7.483314774

Simplifying
x + -4 = 7.483314774

Reorder the terms:
-4 + x = 7.483314774

Solving
-4 + x = 7.483314774

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 7.483314774 + 4

Combine like terms: -4 + 4 = 0
0 + x = 7.483314774 + 4
x = 7.483314774 + 4

Combine like terms: 7.483314774 + 4 = 11.483314774
x = 11.483314774

Simplifying
x = 11.483314774


Subproblem 2
x + -4 = -7.483314774

Simplifying
x + -4 = -7.483314774

Reorder the terms:
-4 + x = -7.483314774

Solving
-4 + x = -7.483314774

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -7.483314774 + 4

Combine like terms: -4 + 4 = 0
0 + x = -7.483314774 + 4
x = -7.483314774 + 4

Combine like terms: -7.483314774 + 4 = -3.483314774
x = -3.483314774

Simplifying
x = -3.483314774


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.483314774, -3.483314774}
Solution
x = {11.483314774, -3.483314774}

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