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Simplifying 6a(a + 3) + -1(a + 3) = 0 Reorder the terms: 6a(3 + a) + -1(a + 3) = 0 (3 * 6a + a * 6a) + -1(a + 3) = 0 (18a + 6a2) + -1(a + 3) = 0 Reorder the terms: 18a + 6a2 + -1(3 + a) = 0 18a + 6a2 + (3 * -1 + a * -1) = 0 18a + 6a2 + (-3 + -1a) = 0 Reorder the terms: -3 + 18a + -1a + 6a2 = 0 Combine like terms: 18a + -1a = 17a -3 + 17a + 6a2 = 0 Solving -3 + 17a + 6a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -1a)(1 + -6a) = 0Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve: Simplifying -3 + -1a = 0 Solving -3 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1a = 0 + 3 -1a = 0 + 3 Combine like terms: 0 + 3 = 3 -1a = 3 Divide each side by '-1'. a = -3 Simplifying a = -3Subproblem 2
Set the factor '(1 + -6a)' equal to zero and attempt to solve: Simplifying 1 + -6a = 0 Solving 1 + -6a = 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 + -6a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6a = 0 + -1 -6a = 0 + -1 Combine like terms: 0 + -1 = -1 -6a = -1 Divide each side by '-6'. a = 0.1666666667 Simplifying a = 0.1666666667Solution
a = {-3, 0.1666666667}
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