(9a+4b)(-9a-5b)=

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Solution for (9a+4b)(-9a-5b)= equation: 


Simplifying
(9a + 4b)(-9a + -5b) = 0

Multiply (9a + 4b) * (-9a + -5b)
(9a * (-9a + -5b) + 4b * (-9a + -5b)) = 0
((-9a * 9a + -5b * 9a) + 4b * (-9a + -5b)) = 0

Reorder the terms:
((-45ab + -81a2) + 4b * (-9a + -5b)) = 0
((-45ab + -81a2) + 4b * (-9a + -5b)) = 0
(-45ab + -81a2 + (-9a * 4b + -5b * 4b)) = 0
(-45ab + -81a2 + (-36ab + -20b2)) = 0

Reorder the terms:
(-45ab + -36ab + -81a2 + -20b2) = 0

Combine like terms: -45ab + -36ab = -81ab
(-81ab + -81a2 + -20b2) = 0

Solving
-81ab + -81a2 + -20b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(81ab + 81a2 + 20b2) = 0

Factor a trinomial.
-1((9a + 4b)(9a + 5b)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(9a + 4b)' equal to zero and attempt to solve:

Simplifying
9a + 4b = 0

Solving
9a + 4b = 0

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

Add '-4b' to each side of the equation.
9a + 4b + -4b = 0 + -4b

Combine like terms: 4b + -4b = 0
9a + 0 = 0 + -4b
9a = 0 + -4b
Remove the zero:
9a = -4b

Divide each side by '9'.
a = -0.4444444444b

Simplifying
a = -0.4444444444b

Subproblem 2
Set the factor '(9a + 5b)' equal to zero and attempt to solve:

Simplifying
9a + 5b = 0

Solving
9a + 5b = 0

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

Add '-5b' to each side of the equation.
9a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
9a + 0 = 0 + -5b
9a = 0 + -5b
Remove the zero:
9a = -5b

Divide each side by '9'.
a = -0.5555555556b

Simplifying
a = -0.5555555556b
Solution
a = {-0.4444444444b, -0.5555555556b}

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