(5a-11b)(9a-2b)=

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Solution for (5a-11b)(9a-2b)= equation: 


Simplifying
(5a + -11b)(9a + -2b) = 0

Multiply (5a + -11b) * (9a + -2b)
(5a * (9a + -2b) + -11b * (9a + -2b)) = 0
((9a * 5a + -2b * 5a) + -11b * (9a + -2b)) = 0

Reorder the terms:
((-10ab + 45a2) + -11b * (9a + -2b)) = 0
((-10ab + 45a2) + -11b * (9a + -2b)) = 0
(-10ab + 45a2 + (9a * -11b + -2b * -11b)) = 0
(-10ab + 45a2 + (-99ab + 22b2)) = 0

Reorder the terms:
(-10ab + -99ab + 45a2 + 22b2) = 0

Combine like terms: -10ab + -99ab = -109ab
(-109ab + 45a2 + 22b2) = 0

Solving
-109ab + 45a2 + 22b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + -11b)(9a + -2b) = 0


Subproblem 1
Set the factor '(5a + -11b)' equal to zero and attempt to solve:

Simplifying
5a + -11b = 0

Solving
5a + -11b = 0

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

Add '11b' to each side of the equation.
5a + -11b + 11b = 0 + 11b

Combine like terms: -11b + 11b = 0
5a + 0 = 0 + 11b
5a = 0 + 11b
Remove the zero:
5a = 11b

Divide each side by '5'.
a = 2.2b

Simplifying
a = 2.2b

Subproblem 2
Set the factor '(9a + -2b)' equal to zero and attempt to solve:

Simplifying
9a + -2b = 0

Solving
9a + -2b = 0

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

Add '2b' to each side of the equation.
9a + -2b + 2b = 0 + 2b

Combine like terms: -2b + 2b = 0
9a + 0 = 0 + 2b
9a = 0 + 2b
Remove the zero:
9a = 2b

Divide each side by '9'.
a = 0.2222222222b

Simplifying
a = 0.2222222222b
Solution
a = {2.2b, 0.2222222222b}

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