(4a+8b)(3a+2b)=

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Solution for (4a+8b)(3a+2b)= equation: 


Simplifying
(4a + 8b)(3a + 2b) = 0

Multiply (4a + 8b) * (3a + 2b)
(4a * (3a + 2b) + 8b * (3a + 2b)) = 0
((3a * 4a + 2b * 4a) + 8b * (3a + 2b)) = 0

Reorder the terms:
((8ab + 12a2) + 8b * (3a + 2b)) = 0
((8ab + 12a2) + 8b * (3a + 2b)) = 0
(8ab + 12a2 + (3a * 8b + 2b * 8b)) = 0
(8ab + 12a2 + (24ab + 16b2)) = 0

Reorder the terms:
(8ab + 24ab + 12a2 + 16b2) = 0

Combine like terms: 8ab + 24ab = 32ab
(32ab + 12a2 + 16b2) = 0

Solving
32ab + 12a2 + 16b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(8ab + 3a2 + 4b2) = 0

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

Ignore the factor 4.

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 '(a + 2b)' equal to zero and attempt to solve:

Simplifying
a + 2b = 0

Solving
a + 2b = 0

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

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

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

Simplifying
a = -2b
Solution
a = {-0.6666666667b, -2b}

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