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Simplifying
(5b + 4t)(5b + -4t) = 0
Multiply (5b + 4t) * (5b + -4t)
(5b * (5b + -4t) + 4t * (5b + -4t)) = 0
((5b * 5b + -4t * 5b) + 4t * (5b + -4t)) = 0
Reorder the terms:
((-20bt + 25b2) + 4t * (5b + -4t)) = 0
((-20bt + 25b2) + 4t * (5b + -4t)) = 0
(-20bt + 25b2 + (5b * 4t + -4t * 4t)) = 0
(-20bt + 25b2 + (20bt + -16t2)) = 0
Reorder the terms:
(-20bt + 20bt + 25b2 + -16t2) = 0
Combine like terms: -20bt + 20bt = 0
(0 + 25b2 + -16t2) = 0
(25b2 + -16t2) = 0
Solving
25b2 + -16t2 = 0
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '16t2' to each side of the equation.
25b2 + -16t2 + 16t2 = 0 + 16t2
Combine like terms: -16t2 + 16t2 = 0
25b2 + 0 = 0 + 16t2
25b2 = 0 + 16t2
Remove the zero:
25b2 = 16t2
Divide each side by '25'.
b2 = 0.64t2
Simplifying
b2 = 0.64t2
Take the square root of each side:
b = {-0.8t, 0.8t}
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