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Simplifying 5a(2a + -5a + -6) + -2a(a + -4) = 0 Reorder the terms: 5a(-6 + 2a + -5a) + -2a(a + -4) = 0 Combine like terms: 2a + -5a = -3a 5a(-6 + -3a) + -2a(a + -4) = 0 (-6 * 5a + -3a * 5a) + -2a(a + -4) = 0 (-30a + -15a2) + -2a(a + -4) = 0 Reorder the terms: -30a + -15a2 + -2a(-4 + a) = 0 -30a + -15a2 + (-4 * -2a + a * -2a) = 0 -30a + -15a2 + (8a + -2a2) = 0 Reorder the terms: -30a + 8a + -15a2 + -2a2 = 0 Combine like terms: -30a + 8a = -22a -22a + -15a2 + -2a2 = 0 Combine like terms: -15a2 + -2a2 = -17a2 -22a + -17a2 = 0 Solving -22a + -17a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1a'. -1a(22 + 17a) = 0 Ignore the factor -1.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 '(22 + 17a)' equal to zero and attempt to solve: Simplifying 22 + 17a = 0 Solving 22 + 17a = 0 Move all terms containing a to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + 17a = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 17a = 0 + -22 17a = 0 + -22 Combine like terms: 0 + -22 = -22 17a = -22 Divide each side by '17'. a = -1.294117647 Simplifying a = -1.294117647Solution
a = {0, -1.294117647}
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