(8x+1)(8x+1)=16

Solution for (8x+1)(8x+1)=16 equation:

Simplifying
(8x + 1)(8x + 1) = 16

Reorder the terms:
(1 + 8x)(8x + 1) = 16

Reorder the terms:
(1 + 8x)(1 + 8x) = 16

Multiply (1 + 8x) * (1 + 8x)
(1(1 + 8x) + 8x * (1 + 8x)) = 16
((1 * 1 + 8x * 1) + 8x * (1 + 8x)) = 16
((1 + 8x) + 8x * (1 + 8x)) = 16
(1 + 8x + (1 * 8x + 8x * 8x)) = 16
(1 + 8x + (8x + 64x2)) = 16

Combine like terms: 8x + 8x = 16x
(1 + 16x + 64x2) = 16

Solving
1 + 16x + 64x2 = 16

Solving for variable 'x'.

Reorder the terms:
1 + -16 + 16x + 64x2 = 16 + -16

Combine like terms: 1 + -16 = -15
-15 + 16x + 64x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-15 + 16x + 64x2 = 0

Factor a trinomial.
(-5 + -8x)(3 + -8x) = 0

Subproblem 1
Set the factor '(-5 + -8x)' equal to zero and attempt to solve:

Simplifying
-5 + -8x = 0

Solving
-5 + -8x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -8x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -8x = 0 + 5
-8x = 0 + 5

Combine like terms: 0 + 5 = 5
-8x = 5

Divide each side by '-8'.
x = -0.625

Simplifying
x = -0.625
Subproblem 2
Set the factor '(3 + -8x)' equal to zero and attempt to solve:

Simplifying
3 + -8x = 0

Solving
3 + -8x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -8x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8x = 0 + -3
-8x = 0 + -3

Combine like terms: 0 + -3 = -3
-8x = -3

Divide each side by '-8'.
x = 0.375

Simplifying
x = 0.375
Solution
x = {-0.625, 0.375}