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

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

Simplifying
(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}