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

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

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

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

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

Multiply (6 + a) * (-1 + 6a)
(6(-1 + 6a) + a(-1 + 6a)) = 0
((-1 * 6 + 6a * 6) + a(-1 + 6a)) = 0
((-6 + 36a) + a(-1 + 6a)) = 0
(-6 + 36a + (-1 * a + 6a * a)) = 0
(-6 + 36a + (-1a + 6a2)) = 0

Combine like terms: 36a + -1a = 35a
(-6 + 35a + 6a2) = 0

Solving
-6 + 35a + 6a2 = 0

Solving for variable 'a'.

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

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

Simplifying
1 + -6a = 0

Solving
1 + -6a = 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 + -6a = 0 + -1

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

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

Divide each side by '-6'.
a = 0.1666666667

Simplifying
a = 0.1666666667
Solution
a = {-6, 0.1666666667}