(4X-1)(2X+1)=

Solution for (4X-1)(2X+1)= 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 = 2X
(-1 + 2X + 8X2) = 0

Solving
-1 + 2X + 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}