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Simplifying 0 = 6a2 + 10a2 + -24a Reorder the terms: 0 = -24a + 6a2 + 10a2 Combine like terms: 6a2 + 10a2 = 16a2 0 = -24a + 16a2 Solving 0 = -24a + 16a2 Solving for variable 'a'. Remove the zero: 24a + -16a2 = -24a + 16a2 + 24a + -16a2 Reorder the terms: 24a + -16a2 = -24a + 24a + 16a2 + -16a2 Combine like terms: -24a + 24a = 0 24a + -16a2 = 0 + 16a2 + -16a2 24a + -16a2 = 16a2 + -16a2 Combine like terms: 16a2 + -16a2 = 0 24a + -16a2 = 0 Factor out the Greatest Common Factor (GCF), '8a'. 8a(3 + -2a) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 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 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Solution
a = {0, 1.5}
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