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Simplifying 5a(3a + -1)(a + 7) = 0 Reorder the terms: 5a(-1 + 3a)(a + 7) = 0 Reorder the terms: 5a(-1 + 3a)(7 + a) = 0 Multiply (-1 + 3a) * (7 + a) 5a(-1(7 + a) + 3a * (7 + a)) = 0 5a((7 * -1 + a * -1) + 3a * (7 + a)) = 0 5a((-7 + -1a) + 3a * (7 + a)) = 0 5a(-7 + -1a + (7 * 3a + a * 3a)) = 0 5a(-7 + -1a + (21a + 3a2)) = 0 Combine like terms: -1a + 21a = 20a 5a(-7 + 20a + 3a2) = 0 (-7 * 5a + 20a * 5a + 3a2 * 5a) = 0 (-35a + 100a2 + 15a3) = 0 Solving -35a + 100a2 + 15a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a'. 5a(-7 + 20a + 3a2) = 0 Factor a trinomial. 5a((-7 + -1a)(1 + -3a)) = 0 Ignore the factor 5.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 '(-7 + -1a)' equal to zero and attempt to solve: Simplifying -7 + -1a = 0 Solving -7 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1a = 0 + 7 -1a = 0 + 7 Combine like terms: 0 + 7 = 7 -1a = 7 Divide each side by '-1'. a = -7 Simplifying a = -7Subproblem 3
Set the factor '(1 + -3a)' equal to zero and attempt to solve: Simplifying 1 + -3a = 0 Solving 1 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3a = 0 + -1 -3a = 0 + -1 Combine like terms: 0 + -1 = -1 -3a = -1 Divide each side by '-3'. a = 0.3333333333 Simplifying a = 0.3333333333Solution
a = {0, -7, 0.3333333333}
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