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Simplifying (7a + -1b)(a + -6b) = 0 Multiply (7a + -1b) * (a + -6b) (7a * (a + -6b) + -1b * (a + -6b)) = 0 ((a * 7a + -6b * 7a) + -1b * (a + -6b)) = 0 Reorder the terms: ((-42ab + 7a2) + -1b * (a + -6b)) = 0 ((-42ab + 7a2) + -1b * (a + -6b)) = 0 (-42ab + 7a2 + (a * -1b + -6b * -1b)) = 0 (-42ab + 7a2 + (-1ab + 6b2)) = 0 Reorder the terms: (-42ab + -1ab + 7a2 + 6b2) = 0 Combine like terms: -42ab + -1ab = -43ab (-43ab + 7a2 + 6b2) = 0 Solving -43ab + 7a2 + 6b2 = 0 Solving for variable 'a'. Factor a trinomial. (a + -6b)(7a + -1b) = 0Subproblem 1
Set the factor '(a + -6b)' equal to zero and attempt to solve: Simplifying a + -6b = 0 Solving a + -6b = 0 Move all terms containing a to the left, all other terms to the right. Add '6b' to each side of the equation. a + -6b + 6b = 0 + 6b Combine like terms: -6b + 6b = 0 a + 0 = 0 + 6b a = 0 + 6b Remove the zero: a = 6b Simplifying a = 6bSubproblem 2
Set the factor '(7a + -1b)' equal to zero and attempt to solve: Simplifying 7a + -1b = 0 Solving 7a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 7a + -1b + b = 0 + b Combine like terms: -1b + b = 0 7a + 0 = 0 + b 7a = 0 + b Remove the zero: 7a = b Divide each side by '7'. a = 0.1428571429b Simplifying a = 0.1428571429bSolution
a = {6b, 0.1428571429b}
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