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

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

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

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

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

Multiply (-3 + 2a) * (4 + a)
(-3(4 + a) + 2a * (4 + a)) = 0
((4 * -3 + a * -3) + 2a * (4 + a)) = 0
((-12 + -3a) + 2a * (4 + a)) = 0
(-12 + -3a + (4 * 2a + a * 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}