3(a-6)=6a(3a+18)

Solution for 3(a-6)=6a(3a+18) equation:

Simplifying
3(a + -6) = 6a(3a + 18)

Reorder the terms:
3(-6 + a) = 6a(3a + 18)
(-6 * 3 + a * 3) = 6a(3a + 18)
(-18 + 3a) = 6a(3a + 18)

Reorder the terms:
-18 + 3a = 6a(18 + 3a)
-18 + 3a = (18 * 6a + 3a * 6a)
-18 + 3a = (108a + 18a2)

Solving
-18 + 3a = 108a + 18a2

Solving for variable 'a'.

Combine like terms: 3a + -108a = -105a
-18 + -105a + -18a2 = 108a + 18a2 + -108a + -18a2

Reorder the terms:
-18 + -105a + -18a2 = 108a + -108a + 18a2 + -18a2

Combine like terms: 108a + -108a = 0
-18 + -105a + -18a2 = 0 + 18a2 + -18a2
-18 + -105a + -18a2 = 18a2 + -18a2

Combine like terms: 18a2 + -18a2 = 0
-18 + -105a + -18a2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(6 + 35a + 6a2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(6 + 35a + 6a2)' equal to zero and attempt to solve:

Simplifying
6 + 35a + 6a2 = 0

Solving
6 + 35a + 6a2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
1 + 5.833333333a + a2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 5.833333333a + -1 + a2 = 0 + -1

Reorder the terms:
1 + -1 + 5.833333333a + a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5.833333333a + a2 = 0 + -1
5.833333333a + a2 = 0 + -1

Combine like terms: 0 + -1 = -1
5.833333333a + a2 = -1

The a term is 5.833333333a.  Take half its coefficient (2.916666667).
Square it (8.506944446) and add it to both sides.

Add '8.506944446' to each side of the equation.
5.833333333a + 8.506944446 + a2 = -1 + 8.506944446

Reorder the terms:
8.506944446 + 5.833333333a + a2 = -1 + 8.506944446

Combine like terms: -1 + 8.506944446 = 7.506944446
8.506944446 + 5.833333333a + a2 = 7.506944446

Factor a perfect square on the left side:
(a + 2.916666667)(a + 2.916666667) = 7.506944446

Calculate the square root of the right side: 2.739880371

Break this problem into two subproblems by setting 
(a + 2.916666667) equal to 2.739880371 and -2.739880371.

Subproblem 1
a + 2.916666667 = 2.739880371

Simplifying
a + 2.916666667 = 2.739880371

Reorder the terms:
2.916666667 + a = 2.739880371

Solving
2.916666667 + a = 2.739880371

Solving for variable 'a'.

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

Add '-2.916666667' to each side of the equation.
2.916666667 + -2.916666667 + a = 2.739880371 + -2.916666667

Combine like terms: 2.916666667 + -2.916666667 = 0.000000000
0.000000000 + a = 2.739880371 + -2.916666667
a = 2.739880371 + -2.916666667

Combine like terms: 2.739880371 + -2.916666667 = -0.176786296
a = -0.176786296

Simplifying
a = -0.176786296

Subproblem 2
a + 2.916666667 = -2.739880371

Simplifying
a + 2.916666667 = -2.739880371

Reorder the terms:
2.916666667 + a = -2.739880371

Solving
2.916666667 + a = -2.739880371

Solving for variable 'a'.

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

Add '-2.916666667' to each side of the equation.
2.916666667 + -2.916666667 + a = -2.739880371 + -2.916666667

Combine like terms: 2.916666667 + -2.916666667 = 0.000000000
0.000000000 + a = -2.739880371 + -2.916666667
a = -2.739880371 + -2.916666667

Combine like terms: -2.739880371 + -2.916666667 = -5.656547038
a = -5.656547038

Simplifying
a = -5.656547038

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.176786296, -5.656547038}
Solution
a = {-0.176786296, -5.656547038}