(2a-1)(8a-3)=0

Solution for (2a-1)(8a-3)=0 equation:

Simplifying
(2a + -1)(8a + -3) = 0

Reorder the terms:
(-1 + 2a)(8a + -3) = 0

Reorder the terms:
(-1 + 2a)(-3 + 8a) = 0

Multiply (-1 + 2a) * (-3 + 8a)
(-1(-3 + 8a) + 2a * (-3 + 8a)) = 0
((-3 * -1 + 8a * -1) + 2a * (-3 + 8a)) = 0
((3 + -8a) + 2a * (-3 + 8a)) = 0
(3 + -8a + (-3 * 2a + 8a * 2a)) = 0
(3 + -8a + (-6a + 16a2)) = 0

Combine like terms: -8a + -6a = -14a
(3 + -14a + 16a2) = 0

Solving
3 + -14a + 16a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + -8a)(1 + -2a) = 0

Subproblem 1
Set the factor '(3 + -8a)' equal to zero and attempt to solve:

Simplifying
3 + -8a = 0

Solving
3 + -8a = 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 + -8a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8a = 0 + -3
-8a = 0 + -3

Combine like terms: 0 + -3 = -3
-8a = -3

Divide each side by '-8'.
a = 0.375

Simplifying
a = 0.375
Subproblem 2
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
Solution
a = {0.375, 0.5}