(3a+4b)(5a+2b)=

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Solution for (3a+4b)(5a+2b)= equation: 


Simplifying
(3a + 4b)(5a + 2b) = 0

Multiply (3a + 4b) * (5a + 2b)
(3a * (5a + 2b) + 4b * (5a + 2b)) = 0
((5a * 3a + 2b * 3a) + 4b * (5a + 2b)) = 0

Reorder the terms:
((6ab + 15a2) + 4b * (5a + 2b)) = 0
((6ab + 15a2) + 4b * (5a + 2b)) = 0
(6ab + 15a2 + (5a * 4b + 2b * 4b)) = 0
(6ab + 15a2 + (20ab + 8b2)) = 0

Reorder the terms:
(6ab + 20ab + 15a2 + 8b2) = 0

Combine like terms: 6ab + 20ab = 26ab
(26ab + 15a2 + 8b2) = 0

Solving
26ab + 15a2 + 8b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + 2b)(3a + 4b) = 0


Subproblem 1
Set the factor '(5a + 2b)' equal to zero and attempt to solve:

Simplifying
5a + 2b = 0

Solving
5a + 2b = 0

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

Add '-2b' to each side of the equation.
5a + 2b + -2b = 0 + -2b

Combine like terms: 2b + -2b = 0
5a + 0 = 0 + -2b
5a = 0 + -2b
Remove the zero:
5a = -2b

Divide each side by '5'.
a = -0.4b

Simplifying
a = -0.4b

Subproblem 2
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
Solution
a = {-0.4b, -1.333333333b}

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