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Simplifying (a + -3)(a + -8a + 5) = 0 Reorder the terms: (-3 + a)(a + -8a + 5) = 0 Reorder the terms: (-3 + a)(5 + a + -8a) = 0 Combine like terms: a + -8a = -7a (-3 + a)(5 + -7a) = 0 Multiply (-3 + a) * (5 + -7a) (-3(5 + -7a) + a(5 + -7a)) = 0 ((5 * -3 + -7a * -3) + a(5 + -7a)) = 0 ((-15 + 21a) + a(5 + -7a)) = 0 (-15 + 21a + (5 * a + -7a * a)) = 0 (-15 + 21a + (5a + -7a2)) = 0 Combine like terms: 21a + 5a = 26a (-15 + 26a + -7a2) = 0 Solving -15 + 26a + -7a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + a)(5 + -7a) = 0Subproblem 1
Set the factor '(-3 + a)' equal to zero and attempt to solve: Simplifying -3 + a = 0 Solving -3 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + a = 0 + 3 a = 0 + 3 Combine like terms: 0 + 3 = 3 a = 3 Simplifying a = 3Subproblem 2
Set the factor '(5 + -7a)' equal to zero and attempt to solve: Simplifying 5 + -7a = 0 Solving 5 + -7a = 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 + -7a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7a = 0 + -5 -7a = 0 + -5 Combine like terms: 0 + -5 = -5 -7a = -5 Divide each side by '-7'. a = 0.7142857143 Simplifying a = 0.7142857143Solution
a = {3, 0.7142857143}
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