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Simplifying 3a2 = 30 + -13a Solving 3a2 = 30 + -13a Solving for variable 'a'. Reorder the terms: -30 + 13a + 3a2 = 30 + -13a + -30 + 13a Reorder the terms: -30 + 13a + 3a2 = 30 + -30 + -13a + 13a Combine like terms: 30 + -30 = 0 -30 + 13a + 3a2 = 0 + -13a + 13a -30 + 13a + 3a2 = -13a + 13a Combine like terms: -13a + 13a = 0 -30 + 13a + 3a2 = 0 Factor a trinomial. (-6 + -1a)(5 + -3a) = 0Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve: Simplifying -6 + -1a = 0 Solving -6 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1a = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1a = 0 + 6 -1a = 0 + 6 Combine like terms: 0 + 6 = 6 -1a = 6 Divide each side by '-1'. a = -6 Simplifying a = -6Subproblem 2
Set the factor '(5 + -3a)' equal to zero and attempt to solve: Simplifying 5 + -3a = 0 Solving 5 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a = 0 + -5 -3a = 0 + -5 Combine like terms: 0 + -5 = -5 -3a = -5 Divide each side by '-3'. a = 1.666666667 Simplifying a = 1.666666667Solution
a = {-6, 1.666666667}
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