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Simplifying 2(8a + -7)(a + -5) = 0 Reorder the terms: 2(-7 + 8a)(a + -5) = 0 Reorder the terms: 2(-7 + 8a)(-5 + a) = 0 Multiply (-7 + 8a) * (-5 + a) 2(-7(-5 + a) + 8a * (-5 + a)) = 0 2((-5 * -7 + a * -7) + 8a * (-5 + a)) = 0 2((35 + -7a) + 8a * (-5 + a)) = 0 2(35 + -7a + (-5 * 8a + a * 8a)) = 0 2(35 + -7a + (-40a + 8a2)) = 0 Combine like terms: -7a + -40a = -47a 2(35 + -47a + 8a2) = 0 (35 * 2 + -47a * 2 + 8a2 * 2) = 0 (70 + -94a + 16a2) = 0 Solving 70 + -94a + 16a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(35 + -47a + 8a2) = 0 Factor a trinomial. 2((7 + -8a)(5 + -1a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -8a)' equal to zero and attempt to solve: Simplifying 7 + -8a = 0 Solving 7 + -8a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -8a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8a = 0 + -7 -8a = 0 + -7 Combine like terms: 0 + -7 = -7 -8a = -7 Divide each side by '-8'. a = 0.875 Simplifying a = 0.875Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve: Simplifying 5 + -1a = 0 Solving 5 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1a = 0 + -5 -1a = 0 + -5 Combine like terms: 0 + -5 = -5 -1a = -5 Divide each side by '-1'. a = 5 Simplifying a = 5Solution
a = {0.875, 5}
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