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

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

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

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

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

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

Combine like terms: -3a + -4a = -7a
(6 + -7a + 2a2) = 0

Solving
6 + -7a + 2a2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
Subproblem 2
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
Solution
a = {1.5, 2}