(4a-1)*(4a-1)-8a+2=0

Solution for (4a-1)*(4a-1)-8a+2=0 equation:

Simplifying
(4a + -1)(4a + -1) + -8a + 2 = 0

Reorder the terms:
(-1 + 4a)(4a + -1) + -8a + 2 = 0

Reorder the terms:
(-1 + 4a)(-1 + 4a) + -8a + 2 = 0

Multiply (-1 + 4a) * (-1 + 4a)
(-1(-1 + 4a) + 4a * (-1 + 4a)) + -8a + 2 = 0
((-1 * -1 + 4a * -1) + 4a * (-1 + 4a)) + -8a + 2 = 0
((1 + -4a) + 4a * (-1 + 4a)) + -8a + 2 = 0
(1 + -4a + (-1 * 4a + 4a * 4a)) + -8a + 2 = 0
(1 + -4a + (-4a + 16a2)) + -8a + 2 = 0

Combine like terms: -4a + -4a = -8a
(1 + -8a + 16a2) + -8a + 2 = 0

Reorder the terms:
1 + 2 + -8a + -8a + 16a2 = 0

Combine like terms: 1 + 2 = 3
3 + -8a + -8a + 16a2 = 0

Combine like terms: -8a + -8a = -16a
3 + -16a + 16a2 = 0

Solving
3 + -16a + 16a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -4a)(3 + -4a) = 0

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 '(3 + -4a)' equal to zero and attempt to solve:

Simplifying
3 + -4a = 0

Solving
3 + -4a = 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 + -4a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4a = 0 + -3
-4a = 0 + -3

Combine like terms: 0 + -3 = -3
-4a = -3

Divide each side by '-4'.
a = 0.75

Simplifying
a = 0.75
Solution
a = {0.25, 0.75}