15a^2-3a-3=0

Solution for 15a^2-3a-3=0 equation:

Simplifying
15a2 + -3a + -3 = 0

Reorder the terms:
-3 + -3a + 15a2 = 0

Solving
-3 + -3a + 15a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -1a + 5a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -1a + 5a2)' equal to zero and attempt to solve:

Simplifying
-1 + -1a + 5a2 = 0

Solving
-1 + -1a + 5a2 = 0

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

Divide each side by '5'.
-0.2 + -0.2a + a2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -0.2a + 0.2 + a2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -0.2a + a2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -0.2a + a2 = 0 + 0.2
-0.2a + a2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-0.2a + a2 = 0.2

The a term is -0.2a.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2a + 0.01 + a2 = 0.2 + 0.01

Reorder the terms:
0.01 + -0.2a + a2 = 0.2 + 0.01

Combine like terms: 0.2 + 0.01 = 0.21
0.01 + -0.2a + a2 = 0.21

Factor a perfect square on the left side:
(a + -0.1)(a + -0.1) = 0.21

Calculate the square root of the right side: 0.458257569

Break this problem into two subproblems by setting 
(a + -0.1) equal to 0.458257569 and -0.458257569.

Subproblem 1
a + -0.1 = 0.458257569

Simplifying
a + -0.1 = 0.458257569

Reorder the terms:
-0.1 + a = 0.458257569

Solving
-0.1 + a = 0.458257569

Solving for variable 'a'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + a = 0.458257569 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + a = 0.458257569 + 0.1
a = 0.458257569 + 0.1

Combine like terms: 0.458257569 + 0.1 = 0.558257569
a = 0.558257569

Simplifying
a = 0.558257569

Subproblem 2
a + -0.1 = -0.458257569

Simplifying
a + -0.1 = -0.458257569

Reorder the terms:
-0.1 + a = -0.458257569

Solving
-0.1 + a = -0.458257569

Solving for variable 'a'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + a = -0.458257569 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + a = -0.458257569 + 0.1
a = -0.458257569 + 0.1

Combine like terms: -0.458257569 + 0.1 = -0.358257569
a = -0.358257569

Simplifying
a = -0.358257569

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.558257569, -0.358257569}
Solution
a = {0.558257569, -0.358257569}