15a^2-3a=-3

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

Simplifying
15a2 + -3a = -3

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

Solving
-3a + 15a2 = -3

Solving for variable 'a'.

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

Combine like terms: -3 + 3 = 0
3 + -3a + 15a2 = 0

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 = -0.19
0.01 + -0.2a + a2 = -0.19

Factor a perfect square on the left side:
(a + -0.1)(a + -0.1) = -0.19

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.