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

Solution for 2(a+6)(a-1)=0 equation:

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

Reorder the terms:
2(6 + a)(a + -1) = 0

Reorder the terms:
2(6 + a)(-1 + a) = 0

Multiply (6 + a) * (-1 + a)
2(6(-1 + a) + a(-1 + a)) = 0
2((-1 * 6 + a * 6) + a(-1 + a)) = 0
2((-6 + 6a) + a(-1 + a)) = 0
2(-6 + 6a + (-1 * a + a * a)) = 0
2(-6 + 6a + (-1a + a2)) = 0

Combine like terms: 6a + -1a = 5a
2(-6 + 5a + a2) = 0
(-6 * 2 + 5a * 2 + a2 * 2) = 0
(-12 + 10a + 2a2) = 0

Solving
-12 + 10a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 5a + a2) = 0

Factor a trinomial.
2((-6 + -1a)(1 + -1a)) = 0

Ignore the factor 2.
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 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

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

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

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

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

Simplifying
a = 1
Solution
a = {-6, 1}