(6a-18)4a=92

Solution for (6a-18)4a=92 equation:

Simplifying
(6a + -18) * 4a = 92

Reorder the terms:
(-18 + 6a) * 4a = 92

Reorder the terms for easier multiplication:
4a(-18 + 6a) = 92
(-18 * 4a + 6a * 4a) = 92
(-72a + 24a2) = 92

Solving
-72a + 24a2 = 92

Solving for variable 'a'.

Reorder the terms:
-92 + -72a + 24a2 = 92 + -92

Combine like terms: 92 + -92 = 0
-92 + -72a + 24a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-23 + -18a + 6a2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-23 + -18a + 6a2)' equal to zero and attempt to solve:

Simplifying
-23 + -18a + 6a2 = 0

Solving
-23 + -18a + 6a2 = 0

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

Divide each side by '6'.
-3.833333333 + -3a + a2 = 0

Move the constant term to the right:

Add '3.833333333' to each side of the equation.
-3.833333333 + -3a + 3.833333333 + a2 = 0 + 3.833333333

Reorder the terms:
-3.833333333 + 3.833333333 + -3a + a2 = 0 + 3.833333333

Combine like terms: -3.833333333 + 3.833333333 = 0.000000000
0.000000000 + -3a + a2 = 0 + 3.833333333
-3a + a2 = 0 + 3.833333333

Combine like terms: 0 + 3.833333333 = 3.833333333
-3a + a2 = 3.833333333

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 = 3.833333333 + 2.25

Reorder the terms:
2.25 + -3a + a2 = 3.833333333 + 2.25

Combine like terms: 3.833333333 + 2.25 = 6.083333333
2.25 + -3a + a2 = 6.083333333

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 6.083333333

Calculate the square root of the right side: 2.466441431

Break this problem into two subproblems by setting 
(a + -1.5) equal to 2.466441431 and -2.466441431.

Subproblem 1
a + -1.5 = 2.466441431

Simplifying
a + -1.5 = 2.466441431

Reorder the terms:
-1.5 + a = 2.466441431

Solving
-1.5 + a = 2.466441431

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 = 2.466441431 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a = 2.466441431 + 1.5
a = 2.466441431 + 1.5

Combine like terms: 2.466441431 + 1.5 = 3.966441431
a = 3.966441431

Simplifying
a = 3.966441431

Subproblem 2
a + -1.5 = -2.466441431

Simplifying
a + -1.5 = -2.466441431

Reorder the terms:
-1.5 + a = -2.466441431

Solving
-1.5 + a = -2.466441431

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 = -2.466441431 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a = -2.466441431 + 1.5
a = -2.466441431 + 1.5

Combine like terms: -2.466441431 + 1.5 = -0.966441431
a = -0.966441431

Simplifying
a = -0.966441431

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.966441431, -0.966441431}
Solution
a = {3.966441431, -0.966441431}