4a^2+12a-72=4

Solution for 4a^2+12a-72=4 equation:

Simplifying
4a2 + 12a + -72 = 4

Reorder the terms:
-72 + 12a + 4a2 = 4

Solving
-72 + 12a + 4a2 = 4

Solving for variable 'a'.

Reorder the terms:
-72 + -4 + 12a + 4a2 = 4 + -4

Combine like terms: -72 + -4 = -76
-76 + 12a + 4a2 = 4 + -4

Combine like terms: 4 + -4 = 0
-76 + 12a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-19 + 3a + a2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-19 + 3a + a2)' equal to zero and attempt to solve:

Simplifying
-19 + 3a + a2 = 0

Solving
-19 + 3a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 3a + 19 + a2 = 0 + 19

Reorder the terms:
-19 + 19 + 3a + a2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 3a + a2 = 0 + 19
3a + a2 = 0 + 19

Combine like terms: 0 + 19 = 19
3a + a2 = 19

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = 19 + 2.25

Reorder the terms:
2.25 + 3a + a2 = 19 + 2.25

Combine like terms: 19 + 2.25 = 21.25
2.25 + 3a + a2 = 21.25

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(a + 1.5) equal to 4.609772229 and -4.609772229.

Subproblem 1
a + 1.5 = 4.609772229

Simplifying
a + 1.5 = 4.609772229

Reorder the terms:
1.5 + a = 4.609772229

Solving
1.5 + a = 4.609772229

Solving for variable 'a'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + a = 4.609772229 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = 4.609772229 + -1.5
a = 4.609772229 + -1.5

Combine like terms: 4.609772229 + -1.5 = 3.109772229
a = 3.109772229

Simplifying
a = 3.109772229

Subproblem 2
a + 1.5 = -4.609772229

Simplifying
a + 1.5 = -4.609772229

Reorder the terms:
1.5 + a = -4.609772229

Solving
1.5 + a = -4.609772229

Solving for variable 'a'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + a = -4.609772229 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = -4.609772229 + -1.5
a = -4.609772229 + -1.5

Combine like terms: -4.609772229 + -1.5 = -6.109772229
a = -6.109772229

Simplifying
a = -6.109772229

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.109772229, -6.109772229}
Solution
a = {3.109772229, -6.109772229}