3a^2+12a-3=0

Solution for 3a^2+12a-3=0 equation:

Simplifying
3a2 + 12a + -3 = 0

Reorder the terms:
-3 + 12a + 3a2 = 0

Solving
-3 + 12a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 4a + a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + 4a + a2)' equal to zero and attempt to solve:

Simplifying
-1 + 4a + a2 = 0

Solving
-1 + 4a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 4a + 1 + a2 = 0 + 1

Reorder the terms:
-1 + 1 + 4a + a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4a + a2 = 0 + 1
4a + a2 = 0 + 1

Combine like terms: 0 + 1 = 1
4a + a2 = 1

The a term is 4a.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4a + 4 + a2 = 1 + 4

Reorder the terms:
4 + 4a + a2 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + 4a + a2 = 5

Factor a perfect square on the left side:
(a + 2)(a + 2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(a + 2) equal to 2.236067978 and -2.236067978.

Subproblem 1
a + 2 = 2.236067978

Simplifying
a + 2 = 2.236067978

Reorder the terms:
2 + a = 2.236067978

Solving
2 + a = 2.236067978

Solving for variable 'a'.

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

Add '-2' to each side of the equation.
2 + -2 + a = 2.236067978 + -2

Combine like terms: 2 + -2 = 0
0 + a = 2.236067978 + -2
a = 2.236067978 + -2

Combine like terms: 2.236067978 + -2 = 0.236067978
a = 0.236067978

Simplifying
a = 0.236067978

Subproblem 2
a + 2 = -2.236067978

Simplifying
a + 2 = -2.236067978

Reorder the terms:
2 + a = -2.236067978

Solving
2 + a = -2.236067978

Solving for variable 'a'.

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

Add '-2' to each side of the equation.
2 + -2 + a = -2.236067978 + -2

Combine like terms: 2 + -2 = 0
0 + a = -2.236067978 + -2
a = -2.236067978 + -2

Combine like terms: -2.236067978 + -2 = -4.236067978
a = -4.236067978

Simplifying
a = -4.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.236067978, -4.236067978}
Solution
a = {0.236067978, -4.236067978}