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Simplifying (7a + 4)(4a + -8) = 0 Reorder the terms: (4 + 7a)(4a + -8) = 0 Reorder the terms: (4 + 7a)(-8 + 4a) = 0 Multiply (4 + 7a) * (-8 + 4a) (4(-8 + 4a) + 7a * (-8 + 4a)) = 0 ((-8 * 4 + 4a * 4) + 7a * (-8 + 4a)) = 0 ((-32 + 16a) + 7a * (-8 + 4a)) = 0 (-32 + 16a + (-8 * 7a + 4a * 7a)) = 0 (-32 + 16a + (-56a + 28a2)) = 0 Combine like terms: 16a + -56a = -40a (-32 + -40a + 28a2) = 0 Solving -32 + -40a + 28a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + -10a + 7a2) = 0 Factor a trinomial. 4((-4 + -7a)(2 + -1a)) = 0 Ignore the factor 4.Subproblem 1
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 = -0.5714285714Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 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 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Solution
a = {-0.5714285714, 2}
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