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Simplifying 3a(4 + -2(4a + -3b)) + -5(-1a(b + -3a) + -2a) = 0 3a(4 + (4a * -2 + -3b * -2)) + -5(-1a(b + -3a) + -2a) = 0 3a(4 + (-8a + 6b)) + -5(-1a(b + -3a) + -2a) = 0 (4 * 3a + -8a * 3a + 6b * 3a) + -5(-1a(b + -3a) + -2a) = 0 Reorder the terms: (12a + 18ab + -24a2) + -5(-1a(b + -3a) + -2a) = 0 (12a + 18ab + -24a2) + -5(-1a(b + -3a) + -2a) = 0 Reorder the terms: 12a + 18ab + -24a2 + -5(-1a(-3a + b) + -2a) = 0 12a + 18ab + -24a2 + -5((-3a * -1a + b * -1a) + -2a) = 0 Reorder the terms: 12a + 18ab + -24a2 + -5((-1ab + 3a2) + -2a) = 0 12a + 18ab + -24a2 + -5((-1ab + 3a2) + -2a) = 0 Reorder the terms: 12a + 18ab + -24a2 + -5(-2a + -1ab + 3a2) = 0 12a + 18ab + -24a2 + (-2a * -5 + -1ab * -5 + 3a2 * -5) = 0 12a + 18ab + -24a2 + (10a + 5ab + -15a2) = 0 Reorder the terms: 12a + 10a + 18ab + 5ab + -24a2 + -15a2 = 0 Combine like terms: 12a + 10a = 22a 22a + 18ab + 5ab + -24a2 + -15a2 = 0 Combine like terms: 18ab + 5ab = 23ab 22a + 23ab + -24a2 + -15a2 = 0 Combine like terms: -24a2 + -15a2 = -39a2 22a + 23ab + -39a2 = 0 Solving 22a + 23ab + -39a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(22 + 23b + -39a) = 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 '(22 + 23b + -39a)' equal to zero and attempt to solve: Simplifying 22 + 23b + -39a = 0 Reorder the terms: 22 + -39a + 23b = 0 Solving 22 + -39a + 23b = 0 Move all terms containing a to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -39a + -22 + 23b = 0 + -22 Reorder the terms: 22 + -22 + -39a + 23b = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -39a + 23b = 0 + -22 -39a + 23b = 0 + -22 Combine like terms: 0 + -22 = -22 -39a + 23b = -22 Add '-23b' to each side of the equation. -39a + 23b + -23b = -22 + -23b Combine like terms: 23b + -23b = 0 -39a + 0 = -22 + -23b -39a = -22 + -23b Divide each side by '-39'. a = 0.5641025641 + 0.5897435897b Simplifying a = 0.5641025641 + 0.5897435897bSolution
a = {0, 0.5641025641 + 0.5897435897b}
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