(4A+5B)(4A-5B)=0

Solution for (4A+5B)(4A-5B)=0 equation:

Simplifying
(4A + 5B)(4A + -5B) = 0

Multiply (4A + 5B) * (4A + -5B)
(4A * (4A + -5B) + 5B * (4A + -5B)) = 0
((4A * 4A + -5B * 4A) + 5B * (4A + -5B)) = 0

Reorder the terms:
((-20AB + 16A2) + 5B * (4A + -5B)) = 0
((-20AB + 16A2) + 5B * (4A + -5B)) = 0
(-20AB + 16A2 + (4A * 5B + -5B * 5B)) = 0
(-20AB + 16A2 + (20AB + -25B2)) = 0

Reorder the terms:
(-20AB + 20AB + 16A2 + -25B2) = 0

Combine like terms: -20AB + 20AB = 0
(0 + 16A2 + -25B2) = 0
(16A2 + -25B2) = 0

Solving
16A2 + -25B2 = 0

Solving for variable 'A'.

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

Add '25B2' to each side of the equation.
16A2 + -25B2 + 25B2 = 0 + 25B2

Combine like terms: -25B2 + 25B2 = 0
16A2 + 0 = 0 + 25B2
16A2 = 0 + 25B2
Remove the zero:
16A2 = 25B2

Divide each side by '16'.
A2 = 1.5625B2

Simplifying
A2 = 1.5625B2

Take the square root of each side:
A = {-1.25B, 1.25B}