6a^2-48a+36=0

Solution for 6a^2-48a+36=0 equation:

Simplifying
6a2 + -48a + 36 = 0

Reorder the terms:
36 + -48a + 6a2 = 0

Solving
36 + -48a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + -8a + a2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(6 + -8a + a2)' equal to zero and attempt to solve:

Simplifying
6 + -8a + a2 = 0

Solving
6 + -8a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -8a + -6 + a2 = 0 + -6

Reorder the terms:
6 + -6 + -8a + a2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -8a + a2 = 0 + -6
-8a + a2 = 0 + -6

Combine like terms: 0 + -6 = -6
-8a + a2 = -6

The a term is -8a.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8a + 16 + a2 = -6 + 16

Reorder the terms:
16 + -8a + a2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + -8a + a2 = 10

Factor a perfect square on the left side:
(a + -4)(a + -4) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(a + -4) equal to 3.16227766 and -3.16227766.

Subproblem 1
a + -4 = 3.16227766

Simplifying
a + -4 = 3.16227766

Reorder the terms:
-4 + a = 3.16227766

Solving
-4 + a = 3.16227766

Solving for variable 'a'.

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

Add '4' to each side of the equation.
-4 + 4 + a = 3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + a = 3.16227766 + 4
a = 3.16227766 + 4

Combine like terms: 3.16227766 + 4 = 7.16227766
a = 7.16227766

Simplifying
a = 7.16227766

Subproblem 2
a + -4 = -3.16227766

Simplifying
a + -4 = -3.16227766

Reorder the terms:
-4 + a = -3.16227766

Solving
-4 + a = -3.16227766

Solving for variable 'a'.

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

Add '4' to each side of the equation.
-4 + 4 + a = -3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + a = -3.16227766 + 4
a = -3.16227766 + 4

Combine like terms: -3.16227766 + 4 = 0.83772234
a = 0.83772234

Simplifying
a = 0.83772234

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {7.16227766, 0.83772234}
Solution
a = {7.16227766, 0.83772234}