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Simplifying (-9a)(-10 + 3a) + 7a(-9 + 3a) = 0 Remove parenthesis around (-9a) -9a(-10 + 3a) + 7a(-9 + 3a) = 0 (-10 * -9a + 3a * -9a) + 7a(-9 + 3a) = 0 (90a + -27a2) + 7a(-9 + 3a) = 0 90a + -27a2 + (-9 * 7a + 3a * 7a) = 0 90a + -27a2 + (-63a + 21a2) = 0 Reorder the terms: 90a + -63a + -27a2 + 21a2 = 0 Combine like terms: 90a + -63a = 27a 27a + -27a2 + 21a2 = 0 Combine like terms: -27a2 + 21a2 = -6a2 27a + -6a2 = 0 Solving 27a + -6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a'. 3a(9 + -2a) = 0 Ignore the factor 3.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 '(9 + -2a)' equal to zero and attempt to solve: Simplifying 9 + -2a = 0 Solving 9 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2a = 0 + -9 -2a = 0 + -9 Combine like terms: 0 + -9 = -9 -2a = -9 Divide each side by '-2'. a = 4.5 Simplifying a = 4.5Solution
a = {0, 4.5}
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