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Simplifying (4a + -1b)(6a + 5b) = 0 Multiply (4a + -1b) * (6a + 5b) (4a * (6a + 5b) + -1b * (6a + 5b)) = 0 ((6a * 4a + 5b * 4a) + -1b * (6a + 5b)) = 0 Reorder the terms: ((20ab + 24a2) + -1b * (6a + 5b)) = 0 ((20ab + 24a2) + -1b * (6a + 5b)) = 0 (20ab + 24a2 + (6a * -1b + 5b * -1b)) = 0 (20ab + 24a2 + (-6ab + -5b2)) = 0 Reorder the terms: (20ab + -6ab + 24a2 + -5b2) = 0 Combine like terms: 20ab + -6ab = 14ab (14ab + 24a2 + -5b2) = 0 Solving 14ab + 24a2 + -5b2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + -1b)(6a + 5b) = 0Subproblem 1
Set the factor '(4a + -1b)' equal to zero and attempt to solve: Simplifying 4a + -1b = 0 Solving 4a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 4a + -1b + b = 0 + b Combine like terms: -1b + b = 0 4a + 0 = 0 + b 4a = 0 + b Remove the zero: 4a = b Divide each side by '4'. a = 0.25b Simplifying a = 0.25bSubproblem 2
Set the factor '(6a + 5b)' equal to zero and attempt to solve: Simplifying 6a + 5b = 0 Solving 6a + 5b = 0 Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. 6a + 5b + -5b = 0 + -5b Combine like terms: 5b + -5b = 0 6a + 0 = 0 + -5b 6a = 0 + -5b Remove the zero: 6a = -5b Divide each side by '6'. a = -0.8333333333b Simplifying a = -0.8333333333bSolution
a = {0.25b, -0.8333333333b}
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