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Simplifying
(2b + 3g)(2b + -3g) = 0
Multiply (2b + 3g) * (2b + -3g)
(2b * (2b + -3g) + 3g * (2b + -3g)) = 0
((2b * 2b + -3g * 2b) + 3g * (2b + -3g)) = 0
Reorder the terms:
((-6bg + 4b2) + 3g * (2b + -3g)) = 0
((-6bg + 4b2) + 3g * (2b + -3g)) = 0
(-6bg + 4b2 + (2b * 3g + -3g * 3g)) = 0
(-6bg + 4b2 + (6bg + -9g2)) = 0
Reorder the terms:
(-6bg + 6bg + 4b2 + -9g2) = 0
Combine like terms: -6bg + 6bg = 0
(0 + 4b2 + -9g2) = 0
(4b2 + -9g2) = 0
Solving
4b2 + -9g2 = 0
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '9g2' to each side of the equation.
4b2 + -9g2 + 9g2 = 0 + 9g2
Combine like terms: -9g2 + 9g2 = 0
4b2 + 0 = 0 + 9g2
4b2 = 0 + 9g2
Remove the zero:
4b2 = 9g2
Divide each side by '4'.
b2 = 2.25g2
Simplifying
b2 = 2.25g2
Take the square root of each side:
b = {-1.5g, 1.5g}
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