(-8a+3b)(2b+3a)=

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Solution for (-8a+3b)(2b+3a)= equation: 


Simplifying
(-8a + 3b)(2b + 3a) = 0

Reorder the terms:
(-8a + 3b)(3a + 2b) = 0

Multiply (-8a + 3b) * (3a + 2b)
(-8a * (3a + 2b) + 3b * (3a + 2b)) = 0
((3a * -8a + 2b * -8a) + 3b * (3a + 2b)) = 0

Reorder the terms:
((-16ab + -24a2) + 3b * (3a + 2b)) = 0
((-16ab + -24a2) + 3b * (3a + 2b)) = 0
(-16ab + -24a2 + (3a * 3b + 2b * 3b)) = 0
(-16ab + -24a2 + (9ab + 6b2)) = 0

Reorder the terms:
(-16ab + 9ab + -24a2 + 6b2) = 0

Combine like terms: -16ab + 9ab = -7ab
(-7ab + -24a2 + 6b2) = 0

Solving
-7ab + -24a2 + 6b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3a + -2b)(8a + -3b) = 0


Subproblem 1
Set the factor '(-3a + -2b)' equal to zero and attempt to solve:

Simplifying
-3a + -2b = 0

Solving
-3a + -2b = 0

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

Add '2b' to each side of the equation.
-3a + -2b + 2b = 0 + 2b

Combine like terms: -2b + 2b = 0
-3a + 0 = 0 + 2b
-3a = 0 + 2b
Remove the zero:
-3a = 2b

Divide each side by '-3'.
a = -0.6666666667b

Simplifying
a = -0.6666666667b

Subproblem 2
Set the factor '(8a + -3b)' equal to zero and attempt to solve:

Simplifying
8a + -3b = 0

Solving
8a + -3b = 0

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

Add '3b' to each side of the equation.
8a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
8a + 0 = 0 + 3b
8a = 0 + 3b
Remove the zero:
8a = 3b

Divide each side by '8'.
a = 0.375b

Simplifying
a = 0.375b
Solution
a = {-0.6666666667b, 0.375b}

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