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Simplifying 4a(7a + -4)(4a + -1) = 0 Reorder the terms: 4a(-4 + 7a)(4a + -1) = 0 Reorder the terms: 4a(-4 + 7a)(-1 + 4a) = 0 Multiply (-4 + 7a) * (-1 + 4a) 4a(-4(-1 + 4a) + 7a * (-1 + 4a)) = 0 4a((-1 * -4 + 4a * -4) + 7a * (-1 + 4a)) = 0 4a((4 + -16a) + 7a * (-1 + 4a)) = 0 4a(4 + -16a + (-1 * 7a + 4a * 7a)) = 0 4a(4 + -16a + (-7a + 28a2)) = 0 Combine like terms: -16a + -7a = -23a 4a(4 + -23a + 28a2) = 0 (4 * 4a + -23a * 4a + 28a2 * 4a) = 0 (16a + -92a2 + 112a3) = 0 Solving 16a + -92a2 + 112a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4a'. 4a(4 + -23a + 28a2) = 0 Factor a trinomial. 4a((1 + -4a)(4 + -7a)) = 0 Ignore the factor 4.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 '(1 + -4a)' equal to zero and attempt to solve: Simplifying 1 + -4a = 0 Solving 1 + -4a = 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 + -4a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4a = 0 + -1 -4a = 0 + -1 Combine like terms: 0 + -1 = -1 -4a = -1 Divide each side by '-4'. a = 0.25 Simplifying a = 0.25Subproblem 3
Set the factor '(4 + -7a)' equal to zero and attempt to solve: Simplifying 4 + -7a = 0 Solving 4 + -7a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7a = 0 + -4 -7a = 0 + -4 Combine like terms: 0 + -4 = -4 -7a = -4 Divide each side by '-7'. a = 0.5714285714 Simplifying a = 0.5714285714Solution
a = {0, 0.25, 0.5714285714}
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