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Simplifying 3a2 + -4a = 20 + -15a Reorder the terms: -4a + 3a2 = 20 + -15a Solving -4a + 3a2 = 20 + -15a Solving for variable 'a'. Reorder the terms: -20 + -4a + 15a + 3a2 = 20 + -15a + -20 + 15a Combine like terms: -4a + 15a = 11a -20 + 11a + 3a2 = 20 + -15a + -20 + 15a Reorder the terms: -20 + 11a + 3a2 = 20 + -20 + -15a + 15a Combine like terms: 20 + -20 = 0 -20 + 11a + 3a2 = 0 + -15a + 15a -20 + 11a + 3a2 = -15a + 15a Combine like terms: -15a + 15a = 0 -20 + 11a + 3a2 = 0 Factor a trinomial. (-5 + -1a)(4 + -3a) = 0Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve: Simplifying -5 + -1a = 0 Solving -5 + -1a = 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 + -1a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1a = 0 + 5 -1a = 0 + 5 Combine like terms: 0 + 5 = 5 -1a = 5 Divide each side by '-1'. a = -5 Simplifying a = -5Subproblem 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 = {-5, 1.333333333}
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