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Simplifying 0 = 3a2 + -13a + 12 Reorder the terms: 0 = 12 + -13a + 3a2 Solving 0 = 12 + -13a + 3a2 Solving for variable 'a'. Combine like terms: 0 + -12 = -12 -12 + 13a + -3a2 = 12 + -13a + 3a2 + -12 + 13a + -3a2 Reorder the terms: -12 + 13a + -3a2 = 12 + -12 + -13a + 13a + 3a2 + -3a2 Combine like terms: 12 + -12 = 0 -12 + 13a + -3a2 = 0 + -13a + 13a + 3a2 + -3a2 -12 + 13a + -3a2 = -13a + 13a + 3a2 + -3a2 Combine like terms: -13a + 13a = 0 -12 + 13a + -3a2 = 0 + 3a2 + -3a2 -12 + 13a + -3a2 = 3a2 + -3a2 Combine like terms: 3a2 + -3a2 = 0 -12 + 13a + -3a2 = 0 Factor a trinomial. (-3 + a)(4 + -3a) = 0Subproblem 1
Set the factor '(-3 + a)' equal to zero and attempt to solve: Simplifying -3 + a = 0 Solving -3 + a = 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 + a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + a = 0 + 3 a = 0 + 3 Combine like terms: 0 + 3 = 3 a = 3 Simplifying a = 3Subproblem 2
Set the factor '(4 + -3a)' equal to zero and attempt to solve: Simplifying 4 + -3a = 0 Solving 4 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a = 0 + -4 -3a = 0 + -4 Combine like terms: 0 + -4 = -4 -3a = -4 Divide each side by '-3'. a = 1.333333333 Simplifying a = 1.333333333Solution
a = {3, 1.333333333}
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