(3a+2b)(2a-3b)=

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Solution for (3a+2b)(2a-3b)= equation: 


Simplifying
(3a + 2b)(2a + -3b) = 0

Multiply (3a + 2b) * (2a + -3b)
(3a * (2a + -3b) + 2b * (2a + -3b)) = 0
((2a * 3a + -3b * 3a) + 2b * (2a + -3b)) = 0

Reorder the terms:
((-9ab + 6a2) + 2b * (2a + -3b)) = 0
((-9ab + 6a2) + 2b * (2a + -3b)) = 0
(-9ab + 6a2 + (2a * 2b + -3b * 2b)) = 0
(-9ab + 6a2 + (4ab + -6b2)) = 0

Reorder the terms:
(-9ab + 4ab + 6a2 + -6b2) = 0

Combine like terms: -9ab + 4ab = -5ab
(-5ab + 6a2 + -6b2) = 0

Solving
-5ab + 6a2 + -6b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -3b)(3a + 2b) = 0


Subproblem 1
Set the factor '(2a + -3b)' equal to zero and attempt to solve:

Simplifying
2a + -3b = 0

Solving
2a + -3b = 0

Move all terms containing a to the left, all other terms to the right.

Add '3b' to each side of the equation.
2a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
2a + 0 = 0 + 3b
2a = 0 + 3b
Remove the zero:
2a = 3b

Divide each side by '2'.
a = 1.5b

Simplifying
a = 1.5b

Subproblem 2
Set the factor '(3a + 2b)' equal to zero and attempt to solve:

Simplifying
3a + 2b = 0

Solving
3a + 2b = 0

Move all terms containing a to the left, all other terms to the right.

Add '-2b' to each side of the equation.
3a + 2b + -2b = 0 + -2b

Combine like terms: 2b + -2b = 0
3a + 0 = 0 + -2b
3a = 0 + -2b
Remove the zero:
3a = -2b

Divide each side by '3'.
a = -0.6666666667b

Simplifying
a = -0.6666666667b
Solution
a = {1.5b, -0.6666666667b}

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