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

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


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

Reorder the terms for easier multiplication:
5 * 5(4a + 3b)(2a + 3b) = 0

Multiply 5 * 5
25(4a + 3b)(2a + 3b) = 0

Multiply (4a + 3b) * (2a + 3b)
25(4a * (2a + 3b) + 3b * (2a + 3b)) = 0
25((2a * 4a + 3b * 4a) + 3b * (2a + 3b)) = 0

Reorder the terms:
25((12ab + 8a2) + 3b * (2a + 3b)) = 0
25((12ab + 8a2) + 3b * (2a + 3b)) = 0
25(12ab + 8a2 + (2a * 3b + 3b * 3b)) = 0
25(12ab + 8a2 + (6ab + 9b2)) = 0

Reorder the terms:
25(12ab + 6ab + 8a2 + 9b2) = 0

Combine like terms: 12ab + 6ab = 18ab
25(18ab + 8a2 + 9b2) = 0
(18ab * 25 + 8a2 * 25 + 9b2 * 25) = 0
(450ab + 200a2 + 225b2) = 0

Solving
450ab + 200a2 + 225b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '25'.
25(18ab + 8a2 + 9b2) = 0

Factor a trinomial.
25((4a + 3b)(2a + 3b)) = 0

Ignore the factor 25.

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

Simplifying
4a + 3b = 0

Solving
4a + 3b = 0

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

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

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

Divide each side by '4'.
a = -0.75b

Simplifying
a = -0.75b

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 = {-0.75b, -1.5b}

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