(4x+1)(2x+1)=0

Solution for (4x+1)(2x+1)=0 equation:

Simplifying
(4x + 1)(2x + 1) = 0

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

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

Multiply (1 + 4x) * (1 + 2x)
(1(1 + 2x) + 4x * (1 + 2x)) = 0
((1 * 1 + 2x * 1) + 4x * (1 + 2x)) = 0
((1 + 2x) + 4x * (1 + 2x)) = 0
(1 + 2x + (1 * 4x + 2x * 4x)) = 0
(1 + 2x + (4x + 8x2)) = 0

Combine like terms: 2x + 4x = 6x
(1 + 6x + 8x2) = 0

Solving
1 + 6x + 8x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4x = 0 + -1

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

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

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

Simplifying
x = -0.25
Solution
x = {-0.5, -0.25}