(4a+2b)(6a-8b)=

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Solution for (4a+2b)(6a-8b)= equation: 


Simplifying
(4a + 2b)(6a + -8b) = 0

Multiply (4a + 2b) * (6a + -8b)
(4a * (6a + -8b) + 2b * (6a + -8b)) = 0
((6a * 4a + -8b * 4a) + 2b * (6a + -8b)) = 0

Reorder the terms:
((-32ab + 24a2) + 2b * (6a + -8b)) = 0
((-32ab + 24a2) + 2b * (6a + -8b)) = 0
(-32ab + 24a2 + (6a * 2b + -8b * 2b)) = 0
(-32ab + 24a2 + (12ab + -16b2)) = 0

Reorder the terms:
(-32ab + 12ab + 24a2 + -16b2) = 0

Combine like terms: -32ab + 12ab = -20ab
(-20ab + 24a2 + -16b2) = 0

Solving
-20ab + 24a2 + -16b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5ab + 6a2 + -4b2) = 0

Factor a trinomial.
4((3a + -4b)(2a + b)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3a + -4b)' equal to zero and attempt to solve:

Simplifying
3a + -4b = 0

Solving
3a + -4b = 0

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

Add '4b' to each side of the equation.
3a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
3a + 0 = 0 + 4b
3a = 0 + 4b
Remove the zero:
3a = 4b

Divide each side by '3'.
a = 1.333333333b

Simplifying
a = 1.333333333b

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

Simplifying
2a + b = 0

Solving
2a + b = 0

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

Add '-1b' to each side of the equation.
2a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
2a + 0 = 0 + -1b
2a = 0 + -1b
Remove the zero:
2a = -1b

Divide each side by '2'.
a = -0.5b

Simplifying
a = -0.5b
Solution
a = {1.333333333b, -0.5b}

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