(7a+b)(7a-b)=0

Solution for (7a+b)(7a-b)=0 equation:

Simplifying
(7a + b)(7a + -1b) = 0

Multiply (7a + b) * (7a + -1b)
(7a * (7a + -1b) + b(7a + -1b)) = 0
((7a * 7a + -1b * 7a) + b(7a + -1b)) = 0

Reorder the terms:
((-7ab + 49a2) + b(7a + -1b)) = 0
((-7ab + 49a2) + b(7a + -1b)) = 0
(-7ab + 49a2 + (7a * b + -1b * b)) = 0
(-7ab + 49a2 + (7ab + -1b2)) = 0

Reorder the terms:
(-7ab + 7ab + 49a2 + -1b2) = 0

Combine like terms: -7ab + 7ab = 0
(0 + 49a2 + -1b2) = 0
(49a2 + -1b2) = 0

Solving
49a2 + -1b2 = 0

Solving for variable 'a'.

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

Add 'b2' to each side of the equation.
49a2 + -1b2 + b2 = 0 + b2

Combine like terms: -1b2 + b2 = 0
49a2 + 0 = 0 + b2
49a2 = 0 + b2
Remove the zero:
49a2 = b2

Divide each side by '49'.
a2 = 0.02040816327b2

Simplifying
a2 = 0.02040816327b2

Take the square root of each side:
a = {-0.142857143b, 0.142857143b}