(4a+2)(a-6)=0

Solution for (4a+2)(a-6)=0 equation:

Simplifying
(4a + 2)(a + -6) = 0

Reorder the terms:
(2 + 4a)(a + -6) = 0

Reorder the terms:
(2 + 4a)(-6 + a) = 0

Multiply (2 + 4a) * (-6 + a)
(2(-6 + a) + 4a * (-6 + a)) = 0
((-6 * 2 + a * 2) + 4a * (-6 + a)) = 0
((-12 + 2a) + 4a * (-6 + a)) = 0
(-12 + 2a + (-6 * 4a + a * 4a)) = 0
(-12 + 2a + (-24a + 4a2)) = 0

Combine like terms: 2a + -24a = -22a
(-12 + -22a + 4a2) = 0

Solving
-12 + -22a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -11a + 2a2) = 0

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

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

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 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 + -2a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2a = 0 + 1
-2a = 0 + 1

Combine like terms: 0 + 1 = 1
-2a = 1

Divide each side by '-2'.
a = -0.5

Simplifying
a = -0.5
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 = {-0.5, 6}