2a^2(4a+1)(4a+1)=

Solution for 2a^2(4a+1)(4a+1)= equation:

Simplifying
2a2(4a + 1)(4a + 1) = 0

Reorder the terms:
2a2(1 + 4a)(4a + 1) = 0

Reorder the terms:
2a2(1 + 4a)(1 + 4a) = 0

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

Combine like terms: 4a + 4a = 8a
2a2(1 + 8a + 16a2) = 0
(1 * 2a2 + 8a * 2a2 + 16a2 * 2a2) = 0
(2a2 + 16a3 + 32a4) = 0

Solving
2a2 + 16a3 + 32a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a2'.
2a2(1 + 8a + 16a2) = 0

Factor a trinomial.
2a2((1 + 4a)(1 + 4a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
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
Subproblem 3
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, -0.25, -0.25}