(2a-3)(4a-5)=0

Solution for (2a-3)(4a-5)=0 equation:

Simplifying
(2a + -3)(4a + -5) = 0

Reorder the terms:
(-3 + 2a)(4a + -5) = 0

Reorder the terms:
(-3 + 2a)(-5 + 4a) = 0

Multiply (-3 + 2a) * (-5 + 4a)
(-3(-5 + 4a) + 2a * (-5 + 4a)) = 0
((-5 * -3 + 4a * -3) + 2a * (-5 + 4a)) = 0
((15 + -12a) + 2a * (-5 + 4a)) = 0
(15 + -12a + (-5 * 2a + 4a * 2a)) = 0
(15 + -12a + (-10a + 8a2)) = 0

Combine like terms: -12a + -10a = -22a
(15 + -22a + 8a2) = 0

Solving
15 + -22a + 8a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5 + -4a)(3 + -2a) = 0

Subproblem 1
Set the factor '(5 + -4a)' equal to zero and attempt to solve:

Simplifying
5 + -4a = 0

Solving
5 + -4a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4a = 0 + -5
-4a = 0 + -5

Combine like terms: 0 + -5 = -5
-4a = -5

Divide each side by '-4'.
a = 1.25

Simplifying
a = 1.25
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 = {1.25, 1.5}