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Simplifying (2a + 3b)(4a + 5b) = 0 Multiply (2a + 3b) * (4a + 5b) (2a * (4a + 5b) + 3b * (4a + 5b)) = 0 ((4a * 2a + 5b * 2a) + 3b * (4a + 5b)) = 0 Reorder the terms: ((10ab + 8a2) + 3b * (4a + 5b)) = 0 ((10ab + 8a2) + 3b * (4a + 5b)) = 0 (10ab + 8a2 + (4a * 3b + 5b * 3b)) = 0 (10ab + 8a2 + (12ab + 15b2)) = 0 Reorder the terms: (10ab + 12ab + 8a2 + 15b2) = 0 Combine like terms: 10ab + 12ab = 22ab (22ab + 8a2 + 15b2) = 0 Solving 22ab + 8a2 + 15b2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + 5b)(2a + 3b) = 0Subproblem 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 = -1.25bSubproblem 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 = -1.5bSolution
a = {-1.25b, -1.5b}
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