(-11a-8b)(-5a-6b)=0

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Solution for (-11a-8b)(-5a-6b)=0 equation: 


Simplifying
(-11a + -8b)(-5a + -6b) = 0

Multiply (-11a + -8b) * (-5a + -6b)
(-11a * (-5a + -6b) + -8b * (-5a + -6b)) = 0
((-5a * -11a + -6b * -11a) + -8b * (-5a + -6b)) = 0

Reorder the terms:
((66ab + 55a2) + -8b * (-5a + -6b)) = 0
((66ab + 55a2) + -8b * (-5a + -6b)) = 0
(66ab + 55a2 + (-5a * -8b + -6b * -8b)) = 0
(66ab + 55a2 + (40ab + 48b2)) = 0

Reorder the terms:
(66ab + 40ab + 55a2 + 48b2) = 0

Combine like terms: 66ab + 40ab = 106ab
(106ab + 55a2 + 48b2) = 0

Solving
106ab + 55a2 + 48b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(11a + 8b)(5a + 6b) = 0


Subproblem 1
Set the factor '(11a + 8b)' equal to zero and attempt to solve:

Simplifying
11a + 8b = 0

Solving
11a + 8b = 0

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

Add '-8b' to each side of the equation.
11a + 8b + -8b = 0 + -8b

Combine like terms: 8b + -8b = 0
11a + 0 = 0 + -8b
11a = 0 + -8b
Remove the zero:
11a = -8b

Divide each side by '11'.
a = -0.7272727273b

Simplifying
a = -0.7272727273b

Subproblem 2
Set the factor '(5a + 6b)' equal to zero and attempt to solve:

Simplifying
5a + 6b = 0

Solving
5a + 6b = 0

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

Add '-6b' to each side of the equation.
5a + 6b + -6b = 0 + -6b

Combine like terms: 6b + -6b = 0
5a + 0 = 0 + -6b
5a = 0 + -6b
Remove the zero:
5a = -6b

Divide each side by '5'.
a = -1.2b

Simplifying
a = -1.2b
Solution
a = {-0.7272727273b, -1.2b}

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