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Simplifying 5a(3a + -4) + -1a(4a + 1) = 0 Reorder the terms: 5a(-4 + 3a) + -1a(4a + 1) = 0 (-4 * 5a + 3a * 5a) + -1a(4a + 1) = 0 (-20a + 15a2) + -1a(4a + 1) = 0 Reorder the terms: -20a + 15a2 + -1a(1 + 4a) = 0 -20a + 15a2 + (1 * -1a + 4a * -1a) = 0 -20a + 15a2 + (-1a + -4a2) = 0 Reorder the terms: -20a + -1a + 15a2 + -4a2 = 0 Combine like terms: -20a + -1a = -21a -21a + 15a2 + -4a2 = 0 Combine like terms: 15a2 + -4a2 = 11a2 -21a + 11a2 = 0 Solving -21a + 11a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-21 + 11a) = 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 '(-21 + 11a)' equal to zero and attempt to solve: Simplifying -21 + 11a = 0 Solving -21 + 11a = 0 Move all terms containing a to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + 11a = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 11a = 0 + 21 11a = 0 + 21 Combine like terms: 0 + 21 = 21 11a = 21 Divide each side by '11'. a = 1.909090909 Simplifying a = 1.909090909Solution
a = {0, 1.909090909}
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