(4ab+5c)(4ab-5c)=0

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Solution for (4ab+5c)(4ab-5c)=0 equation: 


Simplifying
(4ab + 5c)(4ab + -5c) = 0

Multiply (4ab + 5c) * (4ab + -5c)
(4ab * (4ab + -5c) + 5c * (4ab + -5c)) = 0
((4ab * 4ab + -5c * 4ab) + 5c * (4ab + -5c)) = 0

Reorder the terms:
((-20abc + 16a2b2) + 5c * (4ab + -5c)) = 0
((-20abc + 16a2b2) + 5c * (4ab + -5c)) = 0
(-20abc + 16a2b2 + (4ab * 5c + -5c * 5c)) = 0
(-20abc + 16a2b2 + (20abc + -25c2)) = 0

Reorder the terms:
(-20abc + 20abc + 16a2b2 + -25c2) = 0

Combine like terms: -20abc + 20abc = 0
(0 + 16a2b2 + -25c2) = 0
(16a2b2 + -25c2) = 0

Solving
16a2b2 + -25c2 = 0

Solving for variable 'a'.

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

Add '25c2' to each side of the equation.
16a2b2 + -25c2 + 25c2 = 0 + 25c2

Combine like terms: -25c2 + 25c2 = 0
16a2b2 + 0 = 0 + 25c2
16a2b2 = 0 + 25c2
Remove the zero:
16a2b2 = 25c2

Divide each side by '16b2'.
a2 = 1.5625b-2c2

Simplifying
a2 = 1.5625b-2c2

Take the square root of each side:
a = {-1.25b-1c, 1.25b-1c}

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