(2a-3)(2a-1)=0

Solution for (2a-3)(2a-1)=0 equation:

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

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

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

Multiply (-3 + 2a) * (-1 + 2a)
(-3(-1 + 2a) + 2a * (-1 + 2a)) = 0
((-1 * -3 + 2a * -3) + 2a * (-1 + 2a)) = 0
((3 + -6a) + 2a * (-1 + 2a)) = 0
(3 + -6a + (-1 * 2a + 2a * 2a)) = 0
(3 + -6a + (-2a + 4a2)) = 0

Combine like terms: -6a + -2a = -8a
(3 + -8a + 4a2) = 0

Solving
3 + -8a + 4a2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
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 = {0.5, 1.5}