(7x+1)(7x+1)=16

Solution for (7x+1)(7x+1)=16 equation:

Simplifying
(7x + 1)(7x + 1) = 16

Reorder the terms:
(1 + 7x)(7x + 1) = 16

Reorder the terms:
(1 + 7x)(1 + 7x) = 16

Multiply (1 + 7x) * (1 + 7x)
(1(1 + 7x) + 7x * (1 + 7x)) = 16
((1 * 1 + 7x * 1) + 7x * (1 + 7x)) = 16
((1 + 7x) + 7x * (1 + 7x)) = 16
(1 + 7x + (1 * 7x + 7x * 7x)) = 16
(1 + 7x + (7x + 49x2)) = 16

Combine like terms: 7x + 7x = 14x
(1 + 14x + 49x2) = 16

Solving
1 + 14x + 49x2 = 16

Solving for variable 'x'.

Reorder the terms:
1 + -16 + 14x + 49x2 = 16 + -16

Combine like terms: 1 + -16 = -15
-15 + 14x + 49x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-15 + 14x + 49x2 = 0

Factor a trinomial.
(-5 + -7x)(3 + -7x) = 0

Subproblem 1
Set the factor '(-5 + -7x)' equal to zero and attempt to solve:

Simplifying
-5 + -7x = 0

Solving
-5 + -7x = 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 + -7x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7x = 0 + 5
-7x = 0 + 5

Combine like terms: 0 + 5 = 5
-7x = 5

Divide each side by '-7'.
x = -0.7142857143

Simplifying
x = -0.7142857143
Subproblem 2
Set the factor '(3 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

Solving
3 + -7x = 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 + -7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7x = 0 + -3
-7x = 0 + -3

Combine like terms: 0 + -3 = -3
-7x = -3

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286
Solution
x = {-0.7142857143, 0.4285714286}