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

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

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

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

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

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

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

Solving
1 + 8a + 16a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + 4a)(1 + 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 '(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
Solution
a = {-0.25, -0.25}