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

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

Simplifying
(2a + 3)(4 + -1a) = 0

Reorder the terms:
(3 + 2a)(4 + -1a) = 0

Multiply (3 + 2a) * (4 + -1a)
(3(4 + -1a) + 2a * (4 + -1a)) = 0
((4 * 3 + -1a * 3) + 2a * (4 + -1a)) = 0
((12 + -3a) + 2a * (4 + -1a)) = 0
(12 + -3a + (4 * 2a + -1a * 2a)) = 0
(12 + -3a + (8a + -2a2)) = 0

Combine like terms: -3a + 8a = 5a
(12 + 5a + -2a2) = 0

Solving
12 + 5a + -2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4 + -1a)(3 + 2a) = 0

Subproblem 1
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Subproblem 2
Set the factor '(3 + 2a)' equal to zero and attempt to solve:

Simplifying
3 + 2a = 0

Solving
3 + 2a = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2a = 0 + -3
2a = 0 + -3

Combine like terms: 0 + -3 = -3
2a = -3

Divide each side by '2'.
a = -1.5

Simplifying
a = -1.5
Solution
a = {4, -1.5}