9a(2a-4)=15

Solution for 9a(2a-4)=15 equation:

Simplifying
9a(2a + -4) = 15

Reorder the terms:
9a(-4 + 2a) = 15
(-4 * 9a + 2a * 9a) = 15
(-36a + 18a2) = 15

Solving
-36a + 18a2 = 15

Solving for variable 'a'.

Reorder the terms:
-15 + -36a + 18a2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -36a + 18a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -12a + 6a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -12a + 6a2)' equal to zero and attempt to solve:

Simplifying
-5 + -12a + 6a2 = 0

Solving
-5 + -12a + 6a2 = 0

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

Divide each side by '6'.
-0.8333333333 + -2a + a2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -2a + 0.8333333333 + a2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -2a + a2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -2a + a2 = 0 + 0.8333333333
-2a + a2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-2a + a2 = 0.8333333333

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = 0.8333333333 + 1

Reorder the terms:
1 + -2a + a2 = 0.8333333333 + 1

Combine like terms: 0.8333333333 + 1 = 1.8333333333
1 + -2a + a2 = 1.8333333333

Factor a perfect square on the left side:
(a + -1)(a + -1) = 1.8333333333

Calculate the square root of the right side: 1.354006401

Break this problem into two subproblems by setting 
(a + -1) equal to 1.354006401 and -1.354006401.

Subproblem 1
a + -1 = 1.354006401

Simplifying
a + -1 = 1.354006401

Reorder the terms:
-1 + a = 1.354006401

Solving
-1 + a = 1.354006401

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = 1.354006401 + 1

Combine like terms: -1 + 1 = 0
0 + a = 1.354006401 + 1
a = 1.354006401 + 1

Combine like terms: 1.354006401 + 1 = 2.354006401
a = 2.354006401

Simplifying
a = 2.354006401

Subproblem 2
a + -1 = -1.354006401

Simplifying
a + -1 = -1.354006401

Reorder the terms:
-1 + a = -1.354006401

Solving
-1 + a = -1.354006401

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = -1.354006401 + 1

Combine like terms: -1 + 1 = 0
0 + a = -1.354006401 + 1
a = -1.354006401 + 1

Combine like terms: -1.354006401 + 1 = -0.354006401
a = -0.354006401

Simplifying
a = -0.354006401

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.354006401, -0.354006401}
Solution
a = {2.354006401, -0.354006401}