4a(a-13)=8a+12

Solution for 4a(a-13)=8a+12 equation:

Simplifying
4a(a + -13) = 8a + 12

Reorder the terms:
4a(-13 + a) = 8a + 12
(-13 * 4a + a * 4a) = 8a + 12
(-52a + 4a2) = 8a + 12

Reorder the terms:
-52a + 4a2 = 12 + 8a

Solving
-52a + 4a2 = 12 + 8a

Solving for variable 'a'.

Reorder the terms:
-12 + -52a + -8a + 4a2 = 12 + 8a + -12 + -8a

Combine like terms: -52a + -8a = -60a
-12 + -60a + 4a2 = 12 + 8a + -12 + -8a

Reorder the terms:
-12 + -60a + 4a2 = 12 + -12 + 8a + -8a

Combine like terms: 12 + -12 = 0
-12 + -60a + 4a2 = 0 + 8a + -8a
-12 + -60a + 4a2 = 8a + -8a

Combine like terms: 8a + -8a = 0
-12 + -60a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -15a + a2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + -15a + a2)' equal to zero and attempt to solve:

Simplifying
-3 + -15a + a2 = 0

Solving
-3 + -15a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -15a + 3 + a2 = 0 + 3

Reorder the terms:
-3 + 3 + -15a + a2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -15a + a2 = 0 + 3
-15a + a2 = 0 + 3

Combine like terms: 0 + 3 = 3
-15a + a2 = 3

The a term is -15a.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15a + 56.25 + a2 = 3 + 56.25

Reorder the terms:
56.25 + -15a + a2 = 3 + 56.25

Combine like terms: 3 + 56.25 = 59.25
56.25 + -15a + a2 = 59.25

Factor a perfect square on the left side:
(a + -7.5)(a + -7.5) = 59.25

Calculate the square root of the right side: 7.697402159

Break this problem into two subproblems by setting 
(a + -7.5) equal to 7.697402159 and -7.697402159.

Subproblem 1
a + -7.5 = 7.697402159

Simplifying
a + -7.5 = 7.697402159

Reorder the terms:
-7.5 + a = 7.697402159

Solving
-7.5 + a = 7.697402159

Solving for variable 'a'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + a = 7.697402159 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + a = 7.697402159 + 7.5
a = 7.697402159 + 7.5

Combine like terms: 7.697402159 + 7.5 = 15.197402159
a = 15.197402159

Simplifying
a = 15.197402159

Subproblem 2
a + -7.5 = -7.697402159

Simplifying
a + -7.5 = -7.697402159

Reorder the terms:
-7.5 + a = -7.697402159

Solving
-7.5 + a = -7.697402159

Solving for variable 'a'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + a = -7.697402159 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + a = -7.697402159 + 7.5
a = -7.697402159 + 7.5

Combine like terms: -7.697402159 + 7.5 = -0.197402159
a = -0.197402159

Simplifying
a = -0.197402159

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {15.197402159, -0.197402159}
Solution
a = {15.197402159, -0.197402159}