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Simplifying
(3a + 2b)(3a + -2b) = 0
Multiply (3a + 2b) * (3a + -2b)
(3a * (3a + -2b) + 2b * (3a + -2b)) = 0
((3a * 3a + -2b * 3a) + 2b * (3a + -2b)) = 0
Reorder the terms:
((-6ab + 9a2) + 2b * (3a + -2b)) = 0
((-6ab + 9a2) + 2b * (3a + -2b)) = 0
(-6ab + 9a2 + (3a * 2b + -2b * 2b)) = 0
(-6ab + 9a2 + (6ab + -4b2)) = 0
Reorder the terms:
(-6ab + 6ab + 9a2 + -4b2) = 0
Combine like terms: -6ab + 6ab = 0
(0 + 9a2 + -4b2) = 0
(9a2 + -4b2) = 0
Solving
9a2 + -4b2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '4b2' to each side of the equation.
9a2 + -4b2 + 4b2 = 0 + 4b2
Combine like terms: -4b2 + 4b2 = 0
9a2 + 0 = 0 + 4b2
9a2 = 0 + 4b2
Remove the zero:
9a2 = 4b2
Divide each side by '9'.
a2 = 0.4444444444b2
Simplifying
a2 = 0.4444444444b2
Take the square root of each side:
a = {-0.666666667b, 0.666666667b}
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