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Simplifying 4a(2a + -5) + -3a(a + 1) = 0 Reorder the terms: 4a(-5 + 2a) + -3a(a + 1) = 0 (-5 * 4a + 2a * 4a) + -3a(a + 1) = 0 (-20a + 8a2) + -3a(a + 1) = 0 Reorder the terms: -20a + 8a2 + -3a(1 + a) = 0 -20a + 8a2 + (1 * -3a + a * -3a) = 0 -20a + 8a2 + (-3a + -3a2) = 0 Reorder the terms: -20a + -3a + 8a2 + -3a2 = 0 Combine like terms: -20a + -3a = -23a -23a + 8a2 + -3a2 = 0 Combine like terms: 8a2 + -3a2 = 5a2 -23a + 5a2 = 0 Solving -23a + 5a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-23 + 5a) = 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 '(-23 + 5a)' equal to zero and attempt to solve: Simplifying -23 + 5a = 0 Solving -23 + 5a = 0 Move all terms containing a to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + 5a = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 5a = 0 + 23 5a = 0 + 23 Combine like terms: 0 + 23 = 23 5a = 23 Divide each side by '5'. a = 4.6 Simplifying a = 4.6Solution
a = {0, 4.6}
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