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Simplifying
(2a + 3b)(2a + -3b) = 0
Multiply (2a + 3b) * (2a + -3b)
(2a * (2a + -3b) + 3b * (2a + -3b)) = 0
((2a * 2a + -3b * 2a) + 3b * (2a + -3b)) = 0
Reorder the terms:
((-6ab + 4a2) + 3b * (2a + -3b)) = 0
((-6ab + 4a2) + 3b * (2a + -3b)) = 0
(-6ab + 4a2 + (2a * 3b + -3b * 3b)) = 0
(-6ab + 4a2 + (6ab + -9b2)) = 0
Reorder the terms:
(-6ab + 6ab + 4a2 + -9b2) = 0
Combine like terms: -6ab + 6ab = 0
(0 + 4a2 + -9b2) = 0
(4a2 + -9b2) = 0
Solving
4a2 + -9b2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '9b2' to each side of the equation.
4a2 + -9b2 + 9b2 = 0 + 9b2
Combine like terms: -9b2 + 9b2 = 0
4a2 + 0 = 0 + 9b2
4a2 = 0 + 9b2
Remove the zero:
4a2 = 9b2
Divide each side by '4'.
a2 = 2.25b2
Simplifying
a2 = 2.25b2
Take the square root of each side:
a = {-1.5b, 1.5b}
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