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Simplifying (5a + 2)(6a + -1) = a + 7a + -2 Reorder the terms: (2 + 5a)(6a + -1) = a + 7a + -2 Reorder the terms: (2 + 5a)(-1 + 6a) = a + 7a + -2 Multiply (2 + 5a) * (-1 + 6a) (2(-1 + 6a) + 5a * (-1 + 6a)) = a + 7a + -2 ((-1 * 2 + 6a * 2) + 5a * (-1 + 6a)) = a + 7a + -2 ((-2 + 12a) + 5a * (-1 + 6a)) = a + 7a + -2 (-2 + 12a + (-1 * 5a + 6a * 5a)) = a + 7a + -2 (-2 + 12a + (-5a + 30a2)) = a + 7a + -2 Combine like terms: 12a + -5a = 7a (-2 + 7a + 30a2) = a + 7a + -2 Reorder the terms: -2 + 7a + 30a2 = -2 + a + 7a Combine like terms: a + 7a = 8a -2 + 7a + 30a2 = -2 + 8a Add '2' to each side of the equation. -2 + 7a + 2 + 30a2 = -2 + 2 + 8a Reorder the terms: -2 + 2 + 7a + 30a2 = -2 + 2 + 8a Combine like terms: -2 + 2 = 0 0 + 7a + 30a2 = -2 + 2 + 8a 7a + 30a2 = -2 + 2 + 8a Combine like terms: -2 + 2 = 0 7a + 30a2 = 0 + 8a 7a + 30a2 = 8a Solving 7a + 30a2 = 8a Solving for variable 'a'. Reorder the terms: 7a + -8a + 30a2 = 8a + -8a Combine like terms: 7a + -8a = -1a -1a + 30a2 = 8a + -8a Combine like terms: 8a + -8a = 0 -1a + 30a2 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-1 + 30a) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-1 + 30a)' equal to zero and attempt to solve: Simplifying -1 + 30a = 0 Solving -1 + 30a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 30a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 30a = 0 + 1 30a = 0 + 1 Combine like terms: 0 + 1 = 1 30a = 1 Divide each side by '30'. a = 0.03333333333 Simplifying a = 0.03333333333Solution
a = {0, 0.03333333333}
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