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

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


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

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

Reorder the terms:
((-6ab + 16a2) + 3b * (8a + -3b)) = 0
((-6ab + 16a2) + 3b * (8a + -3b)) = 0
(-6ab + 16a2 + (8a * 3b + -3b * 3b)) = 0
(-6ab + 16a2 + (24ab + -9b2)) = 0

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

Combine like terms: -6ab + 24ab = 18ab
(18ab + 16a2 + -9b2) = 0

Solving
18ab + 16a2 + -9b2 = 0

Solving for variable 'a'.

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


Subproblem 1
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

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

Simplifying
2a + 3b = 0

Solving
2a + 3b = 0

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

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

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

Divide each side by '2'.
a = -1.5b

Simplifying
a = -1.5b
Solution
a = {0.375b, -1.5b}

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