8x=1+16x^2

Solution for 8x=1+16x^2 equation:

Simplifying
8x = 1 + 16x2

Solving
8x = 1 + 16x2

Solving for variable 'x'.

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

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

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

Combine like terms: 16x2 + -16x2 = 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}