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Simplifying (5a + -1b)(8a + 3b) = 0 Multiply (5a + -1b) * (8a + 3b) (5a * (8a + 3b) + -1b * (8a + 3b)) = 0 ((8a * 5a + 3b * 5a) + -1b * (8a + 3b)) = 0 Reorder the terms: ((15ab + 40a2) + -1b * (8a + 3b)) = 0 ((15ab + 40a2) + -1b * (8a + 3b)) = 0 (15ab + 40a2 + (8a * -1b + 3b * -1b)) = 0 (15ab + 40a2 + (-8ab + -3b2)) = 0 Reorder the terms: (15ab + -8ab + 40a2 + -3b2) = 0 Combine like terms: 15ab + -8ab = 7ab (7ab + 40a2 + -3b2) = 0 Solving 7ab + 40a2 + -3b2 = 0 Solving for variable 'a'. Factor a trinomial. (5a + -1b)(8a + 3b) = 0Subproblem 1
Set the factor '(5a + -1b)' equal to zero and attempt to solve: Simplifying 5a + -1b = 0 Solving 5a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 5a + -1b + b = 0 + b Combine like terms: -1b + b = 0 5a + 0 = 0 + b 5a = 0 + b Remove the zero: 5a = b Divide each side by '5'. a = 0.2b Simplifying a = 0.2bSubproblem 2
Set the factor '(8a + 3b)' equal to zero and attempt to solve: Simplifying 8a + 3b = 0 Solving 8a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 8a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 8a + 0 = 0 + -3b 8a = 0 + -3b Remove the zero: 8a = -3b Divide each side by '8'. a = -0.375b Simplifying a = -0.375bSolution
a = {0.2b, -0.375b}
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