2a^2+12a-3=5

Solution for 2a^2+12a-3=5 equation:

Simplifying
2a2 + 12a + -3 = 5

Reorder the terms:
-3 + 12a + 2a2 = 5

Solving
-3 + 12a + 2a2 = 5

Solving for variable 'a'.

Reorder the terms:
-3 + -5 + 12a + 2a2 = 5 + -5

Combine like terms: -3 + -5 = -8
-8 + 12a + 2a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-8 + 12a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 6a + a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + 6a + a2)' equal to zero and attempt to solve:

Simplifying
-4 + 6a + a2 = 0

Solving
-4 + 6a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 6a + 4 + a2 = 0 + 4

Reorder the terms:
-4 + 4 + 6a + a2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 6a + a2 = 0 + 4
6a + a2 = 0 + 4

Combine like terms: 0 + 4 = 4
6a + a2 = 4

The a term is 6a.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6a + 9 + a2 = 4 + 9

Reorder the terms:
9 + 6a + a2 = 4 + 9

Combine like terms: 4 + 9 = 13
9 + 6a + a2 = 13

Factor a perfect square on the left side:
(a + 3)(a + 3) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(a + 3) equal to 3.605551275 and -3.605551275.

Subproblem 1
a + 3 = 3.605551275

Simplifying
a + 3 = 3.605551275

Reorder the terms:
3 + a = 3.605551275

Solving
3 + a = 3.605551275

Solving for variable 'a'.

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

Add '-3' to each side of the equation.
3 + -3 + a = 3.605551275 + -3

Combine like terms: 3 + -3 = 0
0 + a = 3.605551275 + -3
a = 3.605551275 + -3

Combine like terms: 3.605551275 + -3 = 0.605551275
a = 0.605551275

Simplifying
a = 0.605551275

Subproblem 2
a + 3 = -3.605551275

Simplifying
a + 3 = -3.605551275

Reorder the terms:
3 + a = -3.605551275

Solving
3 + a = -3.605551275

Solving for variable 'a'.

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

Add '-3' to each side of the equation.
3 + -3 + a = -3.605551275 + -3

Combine like terms: 3 + -3 = 0
0 + a = -3.605551275 + -3
a = -3.605551275 + -3

Combine like terms: -3.605551275 + -3 = -6.605551275
a = -6.605551275

Simplifying
a = -6.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.605551275, -6.605551275}
Solution
a = {0.605551275, -6.605551275}