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Simplifying
(3b + 4g)(3b + -4g) = 0
Multiply (3b + 4g) * (3b + -4g)
(3b * (3b + -4g) + 4g * (3b + -4g)) = 0
((3b * 3b + -4g * 3b) + 4g * (3b + -4g)) = 0
Reorder the terms:
((-12bg + 9b2) + 4g * (3b + -4g)) = 0
((-12bg + 9b2) + 4g * (3b + -4g)) = 0
(-12bg + 9b2 + (3b * 4g + -4g * 4g)) = 0
(-12bg + 9b2 + (12bg + -16g2)) = 0
Reorder the terms:
(-12bg + 12bg + 9b2 + -16g2) = 0
Combine like terms: -12bg + 12bg = 0
(0 + 9b2 + -16g2) = 0
(9b2 + -16g2) = 0
Solving
9b2 + -16g2 = 0
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '16g2' to each side of the equation.
9b2 + -16g2 + 16g2 = 0 + 16g2
Combine like terms: -16g2 + 16g2 = 0
9b2 + 0 = 0 + 16g2
9b2 = 0 + 16g2
Remove the zero:
9b2 = 16g2
Divide each side by '9'.
b2 = 1.777777778g2
Simplifying
b2 = 1.777777778g2
Take the square root of each side:
b = {-1.333333333g, 1.333333333g}
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