8x(1+2x)=-1

Solution for 8x(1+2x)=-1 equation:

Simplifying
8x(1 + 2x) = -1
(1 * 8x + 2x * 8x) = -1
(8x + 16x2) = -1

Solving
8x + 16x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + 8x + 16x2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 8x + 16x2 = 0

Factor a trinomial.
(1 + 4x)(1 + 4x) = 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 + 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 = {-0.25, -0.25}