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

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

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

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

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

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

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

Solving
-1 + -2x + 8x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-0.25, 0.5}