(4a+9b)(-6a+5b)=

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Solution for (4a+9b)(-6a+5b)= equation: 


Simplifying
(4a + 9b)(-6a + 5b) = 0

Multiply (4a + 9b) * (-6a + 5b)
(4a * (-6a + 5b) + 9b * (-6a + 5b)) = 0
((-6a * 4a + 5b * 4a) + 9b * (-6a + 5b)) = 0

Reorder the terms:
((20ab + -24a2) + 9b * (-6a + 5b)) = 0
((20ab + -24a2) + 9b * (-6a + 5b)) = 0
(20ab + -24a2 + (-6a * 9b + 5b * 9b)) = 0
(20ab + -24a2 + (-54ab + 45b2)) = 0

Reorder the terms:
(20ab + -54ab + -24a2 + 45b2) = 0

Combine like terms: 20ab + -54ab = -34ab
(-34ab + -24a2 + 45b2) = 0

Solving
-34ab + -24a2 + 45b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-4a + -9b)(6a + -5b) = 0


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

Simplifying
-4a + -9b = 0

Solving
-4a + -9b = 0

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

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

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

Divide each side by '-4'.
a = -2.25b

Simplifying
a = -2.25b

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

Simplifying
6a + -5b = 0

Solving
6a + -5b = 0

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

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

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

Divide each side by '6'.
a = 0.8333333333b

Simplifying
a = 0.8333333333b
Solution
a = {-2.25b, 0.8333333333b}

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