3a^2+6a-72=3

Solution for 3a^2+6a-72=3 equation:

Simplifying
3a2 + 6a + -72 = 3

Reorder the terms:
-72 + 6a + 3a2 = 3

Solving
-72 + 6a + 3a2 = 3

Solving for variable 'a'.

Reorder the terms:
-72 + -3 + 6a + 3a2 = 3 + -3

Combine like terms: -72 + -3 = -75
-75 + 6a + 3a2 = 3 + -3

Combine like terms: 3 + -3 = 0
-75 + 6a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-25 + 2a + a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-25 + 2a + a2)' equal to zero and attempt to solve:

Simplifying
-25 + 2a + a2 = 0

Solving
-25 + 2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 2a + 25 + a2 = 0 + 25

Reorder the terms:
-25 + 25 + 2a + a2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 2a + a2 = 0 + 25
2a + a2 = 0 + 25

Combine like terms: 0 + 25 = 25
2a + a2 = 25

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = 25 + 1

Reorder the terms:
1 + 2a + a2 = 25 + 1

Combine like terms: 25 + 1 = 26
1 + 2a + a2 = 26

Factor a perfect square on the left side:
(a + 1)(a + 1) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(a + 1) equal to 5.099019514 and -5.099019514.

Subproblem 1
a + 1 = 5.099019514

Simplifying
a + 1 = 5.099019514

Reorder the terms:
1 + a = 5.099019514

Solving
1 + a = 5.099019514

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = 5.099019514 + -1

Combine like terms: 1 + -1 = 0
0 + a = 5.099019514 + -1
a = 5.099019514 + -1

Combine like terms: 5.099019514 + -1 = 4.099019514
a = 4.099019514

Simplifying
a = 4.099019514

Subproblem 2
a + 1 = -5.099019514

Simplifying
a + 1 = -5.099019514

Reorder the terms:
1 + a = -5.099019514

Solving
1 + a = -5.099019514

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = -5.099019514 + -1

Combine like terms: 1 + -1 = 0
0 + a = -5.099019514 + -1
a = -5.099019514 + -1

Combine like terms: -5.099019514 + -1 = -6.099019514
a = -6.099019514

Simplifying
a = -6.099019514

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.099019514, -6.099019514}
Solution
a = {4.099019514, -6.099019514}