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Simplifying 30a2 = 12a + 96 Reorder the terms: 30a2 = 96 + 12a Solving 30a2 = 96 + 12a Solving for variable 'a'. Reorder the terms: -96 + -12a + 30a2 = 96 + 12a + -96 + -12a Reorder the terms: -96 + -12a + 30a2 = 96 + -96 + 12a + -12a Combine like terms: 96 + -96 = 0 -96 + -12a + 30a2 = 0 + 12a + -12a -96 + -12a + 30a2 = 12a + -12a Combine like terms: 12a + -12a = 0 -96 + -12a + 30a2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-16 + -2a + 5a2) = 0 Factor a trinomial. 6((-8 + -5a)(2 + -1a)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-8 + -5a)' equal to zero and attempt to solve: Simplifying -8 + -5a = 0 Solving -8 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -5a = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5a = 0 + 8 -5a = 0 + 8 Combine like terms: 0 + 8 = 8 -5a = 8 Divide each side by '-5'. a = -1.6 Simplifying a = -1.6Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Solution
a = {-1.6, 2}
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