6x^2+12x-140=0

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Solution for 6x^2+12x-140=0 equation: 


Simplifying
6x2 + 12x + -140 = 0

Reorder the terms:
-140 + 12x + 6x2 = 0

Solving
-140 + 12x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-70 + 6x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-70 + 6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-70 + 6x + 3x2 = 0

Solving
-70 + 6x + 3x2 = 0

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

Divide each side by '3'.
-23.33333333 + 2x + x2 = 0

Move the constant term to the right:

Add '23.33333333' to each side of the equation.
-23.33333333 + 2x + 23.33333333 + x2 = 0 + 23.33333333

Reorder the terms:
-23.33333333 + 23.33333333 + 2x + x2 = 0 + 23.33333333

Combine like terms: -23.33333333 + 23.33333333 = 0.00000000
0.00000000 + 2x + x2 = 0 + 23.33333333
2x + x2 = 0 + 23.33333333

Combine like terms: 0 + 23.33333333 = 23.33333333
2x + x2 = 23.33333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 23.33333333 + 1

Reorder the terms:
1 + 2x + x2 = 23.33333333 + 1

Combine like terms: 23.33333333 + 1 = 24.33333333
1 + 2x + x2 = 24.33333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 24.33333333

Calculate the square root of the right side: 4.932882862

Break this problem into two subproblems by setting 
(x + 1) equal to 4.932882862 and -4.932882862.


Subproblem 1
x + 1 = 4.932882862

Simplifying
x + 1 = 4.932882862

Reorder the terms:
1 + x = 4.932882862

Solving
1 + x = 4.932882862

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 4.932882862 + -1

Combine like terms: 1 + -1 = 0
0 + x = 4.932882862 + -1
x = 4.932882862 + -1

Combine like terms: 4.932882862 + -1 = 3.932882862
x = 3.932882862

Simplifying
x = 3.932882862


Subproblem 2
x + 1 = -4.932882862

Simplifying
x + 1 = -4.932882862

Reorder the terms:
1 + x = -4.932882862

Solving
1 + x = -4.932882862

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -4.932882862 + -1

Combine like terms: 1 + -1 = 0
0 + x = -4.932882862 + -1
x = -4.932882862 + -1

Combine like terms: -4.932882862 + -1 = -5.932882862
x = -5.932882862

Simplifying
x = -5.932882862


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.932882862, -5.932882862}
Solution
x = {3.932882862, -5.932882862}

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