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Simplifying
(3b + 5g)(3b + -5g) = 0
Multiply (3b + 5g) * (3b + -5g)
(3b * (3b + -5g) + 5g * (3b + -5g)) = 0
((3b * 3b + -5g * 3b) + 5g * (3b + -5g)) = 0
Reorder the terms:
((-15bg + 9b2) + 5g * (3b + -5g)) = 0
((-15bg + 9b2) + 5g * (3b + -5g)) = 0
(-15bg + 9b2 + (3b * 5g + -5g * 5g)) = 0
(-15bg + 9b2 + (15bg + -25g2)) = 0
Reorder the terms:
(-15bg + 15bg + 9b2 + -25g2) = 0
Combine like terms: -15bg + 15bg = 0
(0 + 9b2 + -25g2) = 0
(9b2 + -25g2) = 0
Solving
9b2 + -25g2 = 0
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '25g2' to each side of the equation.
9b2 + -25g2 + 25g2 = 0 + 25g2
Combine like terms: -25g2 + 25g2 = 0
9b2 + 0 = 0 + 25g2
9b2 = 0 + 25g2
Remove the zero:
9b2 = 25g2
Divide each side by '9'.
b2 = 2.777777778g2
Simplifying
b2 = 2.777777778g2
Take the square root of each side:
b = {-1.666666667g, 1.666666667g}
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