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Simplifying (4a + b)(5a + 2b) = 0 Multiply (4a + b) * (5a + 2b) (4a * (5a + 2b) + b(5a + 2b)) = 0 ((5a * 4a + 2b * 4a) + b(5a + 2b)) = 0 Reorder the terms: ((8ab + 20a2) + b(5a + 2b)) = 0 ((8ab + 20a2) + b(5a + 2b)) = 0 (8ab + 20a2 + (5a * b + 2b * b)) = 0 (8ab + 20a2 + (5ab + 2b2)) = 0 Reorder the terms: (8ab + 5ab + 20a2 + 2b2) = 0 Combine like terms: 8ab + 5ab = 13ab (13ab + 20a2 + 2b2) = 0 Solving 13ab + 20a2 + 2b2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + b)(5a + 2b) = 0Subproblem 1
Set the factor '(4a + b)' equal to zero and attempt to solve: Simplifying 4a + b = 0 Solving 4a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 4a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 4a + 0 = 0 + -1b 4a = 0 + -1b Remove the zero: 4a = -1b Divide each side by '4'. a = -0.25b Simplifying a = -0.25bSubproblem 2
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 = -0.4bSolution
a = {-0.25b, -0.4b}
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