6a(5a-6)=156

Solution for 6a(5a-6)=156 equation:

Simplifying
6a(5a + -6) = 156

Reorder the terms:
6a(-6 + 5a) = 156
(-6 * 6a + 5a * 6a) = 156
(-36a + 30a2) = 156

Solving
-36a + 30a2 = 156

Solving for variable 'a'.

Reorder the terms:
-156 + -36a + 30a2 = 156 + -156

Combine like terms: 156 + -156 = 0
-156 + -36a + 30a2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-26 + -6a + 5a2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-26 + -6a + 5a2)' equal to zero and attempt to solve:

Simplifying
-26 + -6a + 5a2 = 0

Solving
-26 + -6a + 5a2 = 0

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

Divide each side by '5'.
-5.2 + -1.2a + a2 = 0

Move the constant term to the right:

Add '5.2' to each side of the equation.
-5.2 + -1.2a + 5.2 + a2 = 0 + 5.2

Reorder the terms:
-5.2 + 5.2 + -1.2a + a2 = 0 + 5.2

Combine like terms: -5.2 + 5.2 = 0.0
0.0 + -1.2a + a2 = 0 + 5.2
-1.2a + a2 = 0 + 5.2

Combine like terms: 0 + 5.2 = 5.2
-1.2a + a2 = 5.2

The a term is -1.2a.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2a + 0.36 + a2 = 5.2 + 0.36

Reorder the terms:
0.36 + -1.2a + a2 = 5.2 + 0.36

Combine like terms: 5.2 + 0.36 = 5.56
0.36 + -1.2a + a2 = 5.56

Factor a perfect square on the left side:
(a + -0.6)(a + -0.6) = 5.56

Calculate the square root of the right side: 2.357965225

Break this problem into two subproblems by setting 
(a + -0.6) equal to 2.357965225 and -2.357965225.

Subproblem 1
a + -0.6 = 2.357965225

Simplifying
a + -0.6 = 2.357965225

Reorder the terms:
-0.6 + a = 2.357965225

Solving
-0.6 + a = 2.357965225

Solving for variable 'a'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + a = 2.357965225 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + a = 2.357965225 + 0.6
a = 2.357965225 + 0.6

Combine like terms: 2.357965225 + 0.6 = 2.957965225
a = 2.957965225

Simplifying
a = 2.957965225

Subproblem 2
a + -0.6 = -2.357965225

Simplifying
a + -0.6 = -2.357965225

Reorder the terms:
-0.6 + a = -2.357965225

Solving
-0.6 + a = -2.357965225

Solving for variable 'a'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + a = -2.357965225 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + a = -2.357965225 + 0.6
a = -2.357965225 + 0.6

Combine like terms: -2.357965225 + 0.6 = -1.757965225
a = -1.757965225

Simplifying
a = -1.757965225

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.957965225, -1.757965225}
Solution
a = {2.957965225, -1.757965225}