(4a-4)(4a-1)=0

Solution for (4a-4)(4a-1)=0 equation:

Simplifying
(4a + -4)(4a + -1) = 0

Reorder the terms:
(-4 + 4a)(4a + -1) = 0

Reorder the terms:
(-4 + 4a)(-1 + 4a) = 0

Multiply (-4 + 4a) * (-1 + 4a)
(-4(-1 + 4a) + 4a * (-1 + 4a)) = 0
((-1 * -4 + 4a * -4) + 4a * (-1 + 4a)) = 0
((4 + -16a) + 4a * (-1 + 4a)) = 0
(4 + -16a + (-1 * 4a + 4a * 4a)) = 0
(4 + -16a + (-4a + 16a2)) = 0

Combine like terms: -16a + -4a = -20a
(4 + -20a + 16a2) = 0

Solving
4 + -20a + 16a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -5a + 4a2) = 0

Factor a trinomial.
4((1 + -4a)(1 + -1a)) = 0

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

Simplifying
1 + -4a = 0

Solving
1 + -4a = 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 + -4a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4a = 0 + -1
-4a = 0 + -1

Combine like terms: 0 + -1 = -1
-4a = -1

Divide each side by '-4'.
a = 0.25

Simplifying
a = 0.25
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 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 + -1a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1a = 0 + -1
-1a = 0 + -1

Combine like terms: 0 + -1 = -1
-1a = -1

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Solution
a = {0.25, 1}