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Simplifying 8(2a + 4)(-6a + -1) = 0 Reorder the terms: 8(4 + 2a)(-6a + -1) = 0 Reorder the terms: 8(4 + 2a)(-1 + -6a) = 0 Multiply (4 + 2a) * (-1 + -6a) 8(4(-1 + -6a) + 2a * (-1 + -6a)) = 0 8((-1 * 4 + -6a * 4) + 2a * (-1 + -6a)) = 0 8((-4 + -24a) + 2a * (-1 + -6a)) = 0 8(-4 + -24a + (-1 * 2a + -6a * 2a)) = 0 8(-4 + -24a + (-2a + -12a2)) = 0 Combine like terms: -24a + -2a = -26a 8(-4 + -26a + -12a2) = 0 (-4 * 8 + -26a * 8 + -12a2 * 8) = 0 (-32 + -208a + -96a2) = 0 Solving -32 + -208a + -96a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-16'. -16(2 + 13a + 6a2) = 0 Factor a trinomial. -16((2 + a)(1 + 6a)) = 0 Ignore the factor -16.Subproblem 1
Set the factor '(2 + a)' equal to zero and attempt to solve: Simplifying 2 + a = 0 Solving 2 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + a = 0 + -2 a = 0 + -2 Combine like terms: 0 + -2 = -2 a = -2 Simplifying a = -2Subproblem 2
Set the factor '(1 + 6a)' equal to zero and attempt to solve: Simplifying 1 + 6a = 0 Solving 1 + 6a = 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 + 6a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6a = 0 + -1 6a = 0 + -1 Combine like terms: 0 + -1 = -1 6a = -1 Divide each side by '6'. a = -0.1666666667 Simplifying a = -0.1666666667Solution
a = {-2, -0.1666666667}
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