a-1=5a(8-3a)

Solution for a-1=5a(8-3a) equation:

Simplifying
a + -1 = 5a(8 + -3a)

Reorder the terms:
-1 + a = 5a(8 + -3a)
-1 + a = (8 * 5a + -3a * 5a)
-1 + a = (40a + -15a2)

Solving
-1 + a = 40a + -15a2

Solving for variable 'a'.

Combine like terms: a + -40a = -39a
-1 + -39a + 15a2 = 40a + -15a2 + -40a + 15a2

Reorder the terms:
-1 + -39a + 15a2 = 40a + -40a + -15a2 + 15a2

Combine like terms: 40a + -40a = 0
-1 + -39a + 15a2 = 0 + -15a2 + 15a2
-1 + -39a + 15a2 = -15a2 + 15a2

Combine like terms: -15a2 + 15a2 = 0
-1 + -39a + 15a2 = 0

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

Divide each side by '15'.
-0.06666666667 + -2.6a + a2 = 0

Move the constant term to the right:

Add '0.06666666667' to each side of the equation.
-0.06666666667 + -2.6a + 0.06666666667 + a2 = 0 + 0.06666666667

Reorder the terms:
-0.06666666667 + 0.06666666667 + -2.6a + a2 = 0 + 0.06666666667

Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000
0.00000000000 + -2.6a + a2 = 0 + 0.06666666667
-2.6a + a2 = 0 + 0.06666666667

Combine like terms: 0 + 0.06666666667 = 0.06666666667
-2.6a + a2 = 0.06666666667

The a term is -2.6a.  Take half its coefficient (-1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
-2.6a + 1.69 + a2 = 0.06666666667 + 1.69

Reorder the terms:
1.69 + -2.6a + a2 = 0.06666666667 + 1.69

Combine like terms: 0.06666666667 + 1.69 = 1.75666666667
1.69 + -2.6a + a2 = 1.75666666667

Factor a perfect square on the left side:
(a + -1.3)(a + -1.3) = 1.75666666667

Calculate the square root of the right side: 1.325393023

Break this problem into two subproblems by setting 
(a + -1.3) equal to 1.325393023 and -1.325393023.

Subproblem 1
a + -1.3 = 1.325393023

Simplifying
a + -1.3 = 1.325393023

Reorder the terms:
-1.3 + a = 1.325393023

Solving
-1.3 + a = 1.325393023

Solving for variable 'a'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + a = 1.325393023 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + a = 1.325393023 + 1.3
a = 1.325393023 + 1.3

Combine like terms: 1.325393023 + 1.3 = 2.625393023
a = 2.625393023

Simplifying
a = 2.625393023

Subproblem 2
a + -1.3 = -1.325393023

Simplifying
a + -1.3 = -1.325393023

Reorder the terms:
-1.3 + a = -1.325393023

Solving
-1.3 + a = -1.325393023

Solving for variable 'a'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + a = -1.325393023 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + a = -1.325393023 + 1.3
a = -1.325393023 + 1.3

Combine like terms: -1.325393023 + 1.3 = -0.025393023
a = -0.025393023

Simplifying
a = -0.025393023

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.625393023, -0.025393023}