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

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Solution for (4a+5b)*(2a+3b)=0 equation: 


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

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

Reorder the terms:
((12ab + 8a2) + 5b * (2a + 3b)) = 0
((12ab + 8a2) + 5b * (2a + 3b)) = 0
(12ab + 8a2 + (2a * 5b + 3b * 5b)) = 0
(12ab + 8a2 + (10ab + 15b2)) = 0

Reorder the terms:
(12ab + 10ab + 8a2 + 15b2) = 0

Combine like terms: 12ab + 10ab = 22ab
(22ab + 8a2 + 15b2) = 0

Solving
22ab + 8a2 + 15b2 = 0

Solving for variable 'a'.

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


Subproblem 1
Set the factor '(4a + 5b)' equal to zero and attempt to solve:

Simplifying
4a + 5b = 0

Solving
4a + 5b = 0

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

Add '-5b' to each side of the equation.
4a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
4a + 0 = 0 + -5b
4a = 0 + -5b
Remove the zero:
4a = -5b

Divide each side by '4'.
a = -1.25b

Simplifying
a = -1.25b

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 = {-1.25b, -1.5b}

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