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Simplifying 2a(a + 4) + -3a(a + 2) = 0 Reorder the terms: 2a(4 + a) + -3a(a + 2) = 0 (4 * 2a + a * 2a) + -3a(a + 2) = 0 (8a + 2a2) + -3a(a + 2) = 0 Reorder the terms: 8a + 2a2 + -3a(2 + a) = 0 8a + 2a2 + (2 * -3a + a * -3a) = 0 8a + 2a2 + (-6a + -3a2) = 0 Reorder the terms: 8a + -6a + 2a2 + -3a2 = 0 Combine like terms: 8a + -6a = 2a 2a + 2a2 + -3a2 = 0 Combine like terms: 2a2 + -3a2 = -1a2 2a + -1a2 = 0 Solving 2a + -1a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(2 + -1a) = 0Subproblem 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 '(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 = {0, 2}
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