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

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


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

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

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

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

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

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

Solving for variable 'a'.

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

Factor a trinomial.
3((a + -1b)(2a + 3b)) = 0

Ignore the factor 3.

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

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

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

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

Simplifying
a = b

Subproblem 2
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
Solution
a = {b, -1.5b}

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