12x^2+72x-280=0

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Solution for 12x^2+72x-280=0 equation: 


Simplifying
12x2 + 72x + -280 = 0

Reorder the terms:
-280 + 72x + 12x2 = 0

Solving
-280 + 72x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-70 + 18x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-70 + 18x + 3x2)' equal to zero and attempt to solve:

Simplifying
-70 + 18x + 3x2 = 0

Solving
-70 + 18x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-23.33333333 + 6x + x2 = 0

Move the constant term to the right:

Add '23.33333333' to each side of the equation.
-23.33333333 + 6x + 23.33333333 + x2 = 0 + 23.33333333

Reorder the terms:
-23.33333333 + 23.33333333 + 6x + x2 = 0 + 23.33333333

Combine like terms: -23.33333333 + 23.33333333 = 0.00000000
0.00000000 + 6x + x2 = 0 + 23.33333333
6x + x2 = 0 + 23.33333333

Combine like terms: 0 + 23.33333333 = 23.33333333
6x + x2 = 23.33333333

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 = 23.33333333 + 9

Reorder the terms:
9 + 6x + x2 = 23.33333333 + 9

Combine like terms: 23.33333333 + 9 = 32.33333333
9 + 6x + x2 = 32.33333333

Factor a perfect square on the left side:
(x + 3)(x + 3) = 32.33333333

Calculate the square root of the right side: 5.686240703

Break this problem into two subproblems by setting 
(x + 3) equal to 5.686240703 and -5.686240703.


Subproblem 1
x + 3 = 5.686240703

Simplifying
x + 3 = 5.686240703

Reorder the terms:
3 + x = 5.686240703

Solving
3 + x = 5.686240703

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 = 5.686240703 + -3

Combine like terms: 3 + -3 = 0
0 + x = 5.686240703 + -3
x = 5.686240703 + -3

Combine like terms: 5.686240703 + -3 = 2.686240703
x = 2.686240703

Simplifying
x = 2.686240703


Subproblem 2
x + 3 = -5.686240703

Simplifying
x + 3 = -5.686240703

Reorder the terms:
3 + x = -5.686240703

Solving
3 + x = -5.686240703

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 = -5.686240703 + -3

Combine like terms: 3 + -3 = 0
0 + x = -5.686240703 + -3
x = -5.686240703 + -3

Combine like terms: -5.686240703 + -3 = -8.686240703
x = -8.686240703

Simplifying
x = -8.686240703


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.686240703, -8.686240703}
Solution
x = {2.686240703, -8.686240703}

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