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

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


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

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

Reorder the terms:
((15ab + 12a2) + 3b * (4a + 5b)) = 0
((15ab + 12a2) + 3b * (4a + 5b)) = 0
(15ab + 12a2 + (4a * 3b + 5b * 3b)) = 0
(15ab + 12a2 + (12ab + 15b2)) = 0

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

Combine like terms: 15ab + 12ab = 27ab
(27ab + 12a2 + 15b2) = 0

Solving
27ab + 12a2 + 15b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9ab + 4a2 + 5b2) = 0

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

Ignore the factor 3.

Subproblem 1

Set the factor '(a + b)' equal to zero and attempt to solve: Simplifying a + b = 0 Solving a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 a + 0 = 0 + -1b a = 0 + -1b Remove the zero: a = -1b Simplifying a = -1b

Subproblem 2

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

Solution

a = {-1b, -1.25b}

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