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Simplifying 8(a + -7)(a + 3) = 0 Reorder the terms: 8(-7 + a)(a + 3) = 0 Reorder the terms: 8(-7 + a)(3 + a) = 0 Multiply (-7 + a) * (3 + a) 8(-7(3 + a) + a(3 + a)) = 0 8((3 * -7 + a * -7) + a(3 + a)) = 0 8((-21 + -7a) + a(3 + a)) = 0 8(-21 + -7a + (3 * a + a * a)) = 0 8(-21 + -7a + (3a + a2)) = 0 Combine like terms: -7a + 3a = -4a 8(-21 + -4a + a2) = 0 (-21 * 8 + -4a * 8 + a2 * 8) = 0 (-168 + -32a + 8a2) = 0 Solving -168 + -32a + 8a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '8'. 8(-21 + -4a + a2) = 0 Factor a trinomial. 8((-3 + -1a)(7 + -1a)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve: Simplifying -3 + -1a = 0 Solving -3 + -1a = 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 + -1a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1a = 0 + 3 -1a = 0 + 3 Combine like terms: 0 + 3 = 3 -1a = 3 Divide each side by '-1'. a = -3 Simplifying a = -3Subproblem 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve: Simplifying 7 + -1a = 0 Solving 7 + -1a = 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 + -1a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1a = 0 + -7 -1a = 0 + -7 Combine like terms: 0 + -7 = -7 -1a = -7 Divide each side by '-1'. a = 7 Simplifying a = 7Solution
a = {-3, 7}
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