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

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

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

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

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

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

Combine like terms: 4a + -3a = 1a
(-6 + 1a + 2a2) = 0

Solving
-6 + 1a + 2a2 = 0

Solving for variable 'a'.

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

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 '(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 = {-2, 1.5}