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Simplifying 6a2 + -12 + -4a = 19a + -32 Reorder the terms: -12 + -4a + 6a2 = 19a + -32 Reorder the terms: -12 + -4a + 6a2 = -32 + 19a Solving -12 + -4a + 6a2 = -32 + 19a Solving for variable 'a'. Reorder the terms: -12 + 32 + -4a + -19a + 6a2 = -32 + 19a + 32 + -19a Combine like terms: -12 + 32 = 20 20 + -4a + -19a + 6a2 = -32 + 19a + 32 + -19a Combine like terms: -4a + -19a = -23a 20 + -23a + 6a2 = -32 + 19a + 32 + -19a Reorder the terms: 20 + -23a + 6a2 = -32 + 32 + 19a + -19a Combine like terms: -32 + 32 = 0 20 + -23a + 6a2 = 0 + 19a + -19a 20 + -23a + 6a2 = 19a + -19a Combine like terms: 19a + -19a = 0 20 + -23a + 6a2 = 0 Factor a trinomial. (4 + -3a)(5 + -2a) = 0Subproblem 1
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 = 1.333333333Subproblem 2
Set the factor '(5 + -2a)' equal to zero and attempt to solve: Simplifying 5 + -2a = 0 Solving 5 + -2a = 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 + -2a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2a = 0 + -5 -2a = 0 + -5 Combine like terms: 0 + -5 = -5 -2a = -5 Divide each side by '-2'. a = 2.5 Simplifying a = 2.5Solution
a = {1.333333333, 2.5}
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