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Simplifying 2a(a + -4)(4a + 2) = 0 Reorder the terms: 2a(-4 + a)(4a + 2) = 0 Reorder the terms: 2a(-4 + a)(2 + 4a) = 0 Multiply (-4 + a) * (2 + 4a) 2a(-4(2 + 4a) + a(2 + 4a)) = 0 2a((2 * -4 + 4a * -4) + a(2 + 4a)) = 0 2a((-8 + -16a) + a(2 + 4a)) = 0 2a(-8 + -16a + (2 * a + 4a * a)) = 0 2a(-8 + -16a + (2a + 4a2)) = 0 Combine like terms: -16a + 2a = -14a 2a(-8 + -14a + 4a2) = 0 (-8 * 2a + -14a * 2a + 4a2 * 2a) = 0 (-16a + -28a2 + 8a3) = 0 Solving -16a + -28a2 + 8a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4a'. 4a(-4 + -7a + 2a2) = 0 Factor a trinomial. 4a((-1 + -2a)(4 + -1a)) = 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 + -2a)' equal to zero and attempt to solve: Simplifying -1 + -2a = 0 Solving -1 + -2a = 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 + -2a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2a = 0 + 1 -2a = 0 + 1 Combine like terms: 0 + 1 = 1 -2a = 1 Divide each side by '-2'. a = -0.5 Simplifying a = -0.5Subproblem 3
Set the factor '(4 + -1a)' equal to zero and attempt to solve: Simplifying 4 + -1a = 0 Solving 4 + -1a = 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 + -1a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1a = 0 + -4 -1a = 0 + -4 Combine like terms: 0 + -4 = -4 -1a = -4 Divide each side by '-1'. a = 4 Simplifying a = 4Solution
a = {0, -0.5, 4}
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