18-6a=4a(a+3)

Solution for 18-6a=4a(a+3) equation:

Simplifying
18 + -6a = 4a(a + 3)

Reorder the terms:
18 + -6a = 4a(3 + a)
18 + -6a = (3 * 4a + a * 4a)
18 + -6a = (12a + 4a2)

Solving
18 + -6a = 12a + 4a2

Solving for variable 'a'.

Combine like terms: -6a + -12a = -18a
18 + -18a + -4a2 = 12a + 4a2 + -12a + -4a2

Reorder the terms:
18 + -18a + -4a2 = 12a + -12a + 4a2 + -4a2

Combine like terms: 12a + -12a = 0
18 + -18a + -4a2 = 0 + 4a2 + -4a2
18 + -18a + -4a2 = 4a2 + -4a2

Combine like terms: 4a2 + -4a2 = 0
18 + -18a + -4a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -9a + -2a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + -9a + -2a2)' equal to zero and attempt to solve:

Simplifying
9 + -9a + -2a2 = 0

Solving
9 + -9a + -2a2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-4.5 + 4.5a + a2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + 4.5a + 4.5 + a2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + 4.5a + a2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 4.5a + a2 = 0 + 4.5
4.5a + a2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
4.5a + a2 = 4.5

The a term is 4.5a.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5a + 5.0625 + a2 = 4.5 + 5.0625

Reorder the terms:
5.0625 + 4.5a + a2 = 4.5 + 5.0625

Combine like terms: 4.5 + 5.0625 = 9.5625
5.0625 + 4.5a + a2 = 9.5625

Factor a perfect square on the left side:
(a + 2.25)(a + 2.25) = 9.5625

Calculate the square root of the right side: 3.092329219

Break this problem into two subproblems by setting 
(a + 2.25) equal to 3.092329219 and -3.092329219.

Subproblem 1
a + 2.25 = 3.092329219

Simplifying
a + 2.25 = 3.092329219

Reorder the terms:
2.25 + a = 3.092329219

Solving
2.25 + a = 3.092329219

Solving for variable 'a'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + a = 3.092329219 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + a = 3.092329219 + -2.25
a = 3.092329219 + -2.25

Combine like terms: 3.092329219 + -2.25 = 0.842329219
a = 0.842329219

Simplifying
a = 0.842329219

Subproblem 2
a + 2.25 = -3.092329219

Simplifying
a + 2.25 = -3.092329219

Reorder the terms:
2.25 + a = -3.092329219

Solving
2.25 + a = -3.092329219

Solving for variable 'a'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + a = -3.092329219 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + a = -3.092329219 + -2.25
a = -3.092329219 + -2.25

Combine like terms: -3.092329219 + -2.25 = -5.342329219
a = -5.342329219

Simplifying
a = -5.342329219

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.842329219, -5.342329219}
Solution
a = {0.842329219, -5.342329219}