(2A+3B)(3B-2A)=0

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Solution for (2A+3B)(3B-2A)=0 equation: 


Simplifying
(2A + 3B)(3B + -2A) = 0

Reorder the terms:
(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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