(3a+5b)(9a-12b)=

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Solution for (3a+5b)(9a-12b)= equation: 


Simplifying
(3a + 5b)(9a + -12b) = 0

Multiply (3a + 5b) * (9a + -12b)
(3a * (9a + -12b) + 5b * (9a + -12b)) = 0
((9a * 3a + -12b * 3a) + 5b * (9a + -12b)) = 0

Reorder the terms:
((-36ab + 27a2) + 5b * (9a + -12b)) = 0
((-36ab + 27a2) + 5b * (9a + -12b)) = 0
(-36ab + 27a2 + (9a * 5b + -12b * 5b)) = 0
(-36ab + 27a2 + (45ab + -60b2)) = 0

Reorder the terms:
(-36ab + 45ab + 27a2 + -60b2) = 0

Combine like terms: -36ab + 45ab = 9ab
(9ab + 27a2 + -60b2) = 0

Solving
9ab + 27a2 + -60b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3ab + 9a2 + -20b2) = 0

Factor a trinomial.
3((3a + -4b)(3a + 5b)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(3a + -4b)' equal to zero and attempt to solve:

Simplifying
3a + -4b = 0

Solving
3a + -4b = 0

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

Add '4b' to each side of the equation.
3a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
3a + 0 = 0 + 4b
3a = 0 + 4b
Remove the zero:
3a = 4b

Divide each side by '3'.
a = 1.333333333b

Simplifying
a = 1.333333333b

Subproblem 2
Set the factor '(3a + 5b)' equal to zero and attempt to solve:

Simplifying
3a + 5b = 0

Solving
3a + 5b = 0

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

Add '-5b' to each side of the equation.
3a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
3a + 0 = 0 + -5b
3a = 0 + -5b
Remove the zero:
3a = -5b

Divide each side by '3'.
a = -1.666666667b

Simplifying
a = -1.666666667b
Solution
a = {1.333333333b, -1.666666667b}

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