(2a+4)(6a-3)=0

Solution for (2a+4)(6a-3)=0 equation:

Simplifying
(2a + 4)(6a + -3) = 0

Reorder the terms:
(4 + 2a)(6a + -3) = 0

Reorder the terms:
(4 + 2a)(-3 + 6a) = 0

Multiply (4 + 2a) * (-3 + 6a)
(4(-3 + 6a) + 2a * (-3 + 6a)) = 0
((-3 * 4 + 6a * 4) + 2a * (-3 + 6a)) = 0
((-12 + 24a) + 2a * (-3 + 6a)) = 0
(-12 + 24a + (-3 * 2a + 6a * 2a)) = 0
(-12 + 24a + (-6a + 12a2)) = 0

Combine like terms: 24a + -6a = 18a
(-12 + 18a + 12a2) = 0

Solving
-12 + 18a + 12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + 3a + 2a2) = 0

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

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

Simplifying
-2 + -1a = 0

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

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

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

Divide each side by '-1'.
a = -2

Simplifying
a = -2
Subproblem 2
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
Solution
a = {-2, 0.5}