(a-6)(8a+1)=0

Solution for (a-6)(8a+1)=0 equation:

Simplifying
(a + -6)(8a + 1) = 0

Reorder the terms:
(-6 + a)(8a + 1) = 0

Reorder the terms:
(-6 + a)(1 + 8a) = 0

Multiply (-6 + a) * (1 + 8a)
(-6(1 + 8a) + a(1 + 8a)) = 0
((1 * -6 + 8a * -6) + a(1 + 8a)) = 0
((-6 + -48a) + a(1 + 8a)) = 0
(-6 + -48a + (1 * a + 8a * a)) = 0
(-6 + -48a + (1a + 8a2)) = 0

Combine like terms: -48a + 1a = -47a
(-6 + -47a + 8a2) = 0

Solving
-6 + -47a + 8a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -8a)(6 + -1a) = 0

Subproblem 1
Set the factor '(-1 + -8a)' equal to zero and attempt to solve:

Simplifying
-1 + -8a = 0

Solving
-1 + -8a = 0

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

Add '1' to each side of the equation.
-1 + 1 + -8a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8a = 0 + 1
-8a = 0 + 1

Combine like terms: 0 + 1 = 1
-8a = 1

Divide each side by '-8'.
a = -0.125

Simplifying
a = -0.125
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-0.125, 6}