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Simplifying (5a + -8)(4 + -6a) = 0 Reorder the terms: (-8 + 5a)(4 + -6a) = 0 Multiply (-8 + 5a) * (4 + -6a) (-8(4 + -6a) + 5a * (4 + -6a)) = 0 ((4 * -8 + -6a * -8) + 5a * (4 + -6a)) = 0 ((-32 + 48a) + 5a * (4 + -6a)) = 0 (-32 + 48a + (4 * 5a + -6a * 5a)) = 0 (-32 + 48a + (20a + -30a2)) = 0 Combine like terms: 48a + 20a = 68a (-32 + 68a + -30a2) = 0 Solving -32 + 68a + -30a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + 34a + -15a2) = 0 Factor a trinomial. 2((-8 + 5a)(2 + -3a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 5a)' equal to zero and attempt to solve: Simplifying -8 + 5a = 0 Solving -8 + 5a = 0 Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 5a = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5a = 0 + 8 5a = 0 + 8 Combine like terms: 0 + 8 = 8 5a = 8 Divide each side by '5'. a = 1.6 Simplifying a = 1.6Subproblem 2
Set the factor '(2 + -3a)' equal to zero and attempt to solve: Simplifying 2 + -3a = 0 Solving 2 + -3a = 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 + -3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3a = 0 + -2 -3a = 0 + -2 Combine like terms: 0 + -2 = -2 -3a = -2 Divide each side by '-3'. a = 0.6666666667 Simplifying a = 0.6666666667Solution
a = {1.6, 0.6666666667}
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