6a^2+2a-2=0

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Solution for 6a^2+2a-2=0 equation: 


Simplifying
6a2 + 2a + -2 = 0

Reorder the terms:
-2 + 2a + 6a2 = 0

Solving
-2 + 2a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + a + 3a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + a + 3a2)' equal to zero and attempt to solve:

Simplifying
-1 + a + 3a2 = 0

Solving
-1 + a + 3a2 = 0

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

Divide each side by '3'.
-0.3333333333 + 0.3333333333a + a2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.3333333333a + 0.3333333333 + a2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.3333333333a + a2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.3333333333a + a2 = 0 + 0.3333333333
0.3333333333a + a2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.3333333333a + a2 = 0.3333333333

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333a + 0.25 + a2 = 0.3333333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333a + a2 = 0.3333333333 + 0.25

Combine like terms: 0.3333333333 + 0.25 = 0.5833333333
0.25 + 0.3333333333a + a2 = 0.5833333333

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 0.5833333333

Calculate the square root of the right side: 0.763762616

Break this problem into two subproblems by setting 
(a + 0.5) equal to 0.763762616 and -0.763762616.


Subproblem 1
a + 0.5 = 0.763762616

Simplifying
a + 0.5 = 0.763762616

Reorder the terms:
0.5 + a = 0.763762616

Solving
0.5 + a = 0.763762616

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = 0.763762616 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 0.763762616 + -0.5
a = 0.763762616 + -0.5

Combine like terms: 0.763762616 + -0.5 = 0.263762616
a = 0.263762616

Simplifying
a = 0.263762616


Subproblem 2
a + 0.5 = -0.763762616

Simplifying
a + 0.5 = -0.763762616

Reorder the terms:
0.5 + a = -0.763762616

Solving
0.5 + a = -0.763762616

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = -0.763762616 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -0.763762616 + -0.5
a = -0.763762616 + -0.5

Combine like terms: -0.763762616 + -0.5 = -1.263762616
a = -1.263762616

Simplifying
a = -1.263762616


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.263762616, -1.263762616}
Solution
a = {0.263762616, -1.263762616}

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