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

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

Simplifying
(4a + 2)(6a + -1a + 2) = 0

Reorder the terms:
(2 + 4a)(6a + -1a + 2) = 0

Reorder the terms:
(2 + 4a)(2 + 6a + -1a) = 0

Combine like terms: 6a + -1a = 5a
(2 + 4a)(2 + 5a) = 0

Multiply (2 + 4a) * (2 + 5a)
(2(2 + 5a) + 4a * (2 + 5a)) = 0
((2 * 2 + 5a * 2) + 4a * (2 + 5a)) = 0
((4 + 10a) + 4a * (2 + 5a)) = 0
(4 + 10a + (2 * 4a + 5a * 4a)) = 0
(4 + 10a + (8a + 20a2)) = 0

Combine like terms: 10a + 8a = 18a
(4 + 18a + 20a2) = 0

Solving
4 + 18a + 20a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 9a + 10a2) = 0

Factor a trinomial.
2((1 + 2a)(2 + 5a)) = 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 '(2 + 5a)' equal to zero and attempt to solve:

Simplifying
2 + 5a = 0

Solving
2 + 5a = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5a = 0 + -2
5a = 0 + -2

Combine like terms: 0 + -2 = -2
5a = -2

Divide each side by '5'.
a = -0.4

Simplifying
a = -0.4
Solution
a = {-0.5, -0.4}