(7x-z)(7x+z)=0

Solution for (7x-z)(7x+z)=0 equation:

Simplifying
(7x + -1z)(7x + z) = 0

Multiply (7x + -1z) * (7x + z)
(7x * (7x + z) + -1z * (7x + z)) = 0
((7x * 7x + z * 7x) + -1z * (7x + z)) = 0

Reorder the terms:
((7xz + 49x2) + -1z * (7x + z)) = 0
((7xz + 49x2) + -1z * (7x + z)) = 0
(7xz + 49x2 + (7x * -1z + z * -1z)) = 0
(7xz + 49x2 + (-7xz + -1z2)) = 0

Reorder the terms:
(7xz + -7xz + 49x2 + -1z2) = 0

Combine like terms: 7xz + -7xz = 0
(0 + 49x2 + -1z2) = 0
(49x2 + -1z2) = 0

Solving
49x2 + -1z2 = 0

Solving for variable 'x'.

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

Add 'z2' to each side of the equation.
49x2 + -1z2 + z2 = 0 + z2

Combine like terms: -1z2 + z2 = 0
49x2 + 0 = 0 + z2
49x2 = 0 + z2
Remove the zero:
49x2 = z2

Divide each side by '49'.
x2 = 0.02040816327z2

Simplifying
x2 = 0.02040816327z2

Take the square root of each side:
x = {-0.142857143z, 0.142857143z}