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Simplifying
(3b + 4d)(3b + -4d) = 0
Multiply (3b + 4d) * (3b + -4d)
(3b * (3b + -4d) + 4d * (3b + -4d)) = 0
((3b * 3b + -4d * 3b) + 4d * (3b + -4d)) = 0
Reorder the terms:
((-12bd + 9b2) + 4d * (3b + -4d)) = 0
((-12bd + 9b2) + 4d * (3b + -4d)) = 0
(-12bd + 9b2 + (3b * 4d + -4d * 4d)) = 0
(-12bd + 9b2 + (12bd + -16d2)) = 0
Reorder the terms:
(-12bd + 12bd + 9b2 + -16d2) = 0
Combine like terms: -12bd + 12bd = 0
(0 + 9b2 + -16d2) = 0
(9b2 + -16d2) = 0
Solving
9b2 + -16d2 = 0
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '16d2' to each side of the equation.
9b2 + -16d2 + 16d2 = 0 + 16d2
Combine like terms: -16d2 + 16d2 = 0
9b2 + 0 = 0 + 16d2
9b2 = 0 + 16d2
Remove the zero:
9b2 = 16d2
Divide each side by '9'.
b2 = 1.777777778d2
Simplifying
b2 = 1.777777778d2
Take the square root of each side:
b = {-1.333333333d, 1.333333333d}
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