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

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Solution for (3a-2b)(3a+3b)=0 equation: 


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

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

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

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

Combine like terms: 9ab + -6ab = 3ab
(3ab + 9a2 + -6b2) = 0

Solving
3ab + 9a2 + -6b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(ab + 3a2 + -2b2) = 0

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

Ignore the factor 3.

Subproblem 1
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

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

Simplifying
a + b = 0

Solving
a + b = 0

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

Add '-1b' to each side of the equation.
a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
a + 0 = 0 + -1b
a = 0 + -1b
Remove the zero:
a = -1b

Simplifying
a = -1b
Solution
a = {0.6666666667b, -1b}

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