(11a-6b)(2a+3b)=

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Solution for (11a-6b)(2a+3b)= equation: 


Simplifying
(11a + -6b)(2a + 3b) = 0

Multiply (11a + -6b) * (2a + 3b)
(11a * (2a + 3b) + -6b * (2a + 3b)) = 0
((2a * 11a + 3b * 11a) + -6b * (2a + 3b)) = 0

Reorder the terms:
((33ab + 22a2) + -6b * (2a + 3b)) = 0
((33ab + 22a2) + -6b * (2a + 3b)) = 0
(33ab + 22a2 + (2a * -6b + 3b * -6b)) = 0
(33ab + 22a2 + (-12ab + -18b2)) = 0

Reorder the terms:
(33ab + -12ab + 22a2 + -18b2) = 0

Combine like terms: 33ab + -12ab = 21ab
(21ab + 22a2 + -18b2) = 0

Solving
21ab + 22a2 + -18b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(11a + -6b)(2a + 3b) = 0


Subproblem 1
Set the factor '(11a + -6b)' equal to zero and attempt to solve:

Simplifying
11a + -6b = 0

Solving
11a + -6b = 0

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

Add '6b' to each side of the equation.
11a + -6b + 6b = 0 + 6b

Combine like terms: -6b + 6b = 0
11a + 0 = 0 + 6b
11a = 0 + 6b
Remove the zero:
11a = 6b

Divide each side by '11'.
a = 0.5454545455b

Simplifying
a = 0.5454545455b

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 = {0.5454545455b, -1.5b}

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