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Simplifying a(a + -3)(a + 7) = 0 Reorder the terms: a(-3 + a)(a + 7) = 0 Reorder the terms: a(-3 + a)(7 + a) = 0 Multiply (-3 + a) * (7 + a) a(-3(7 + a) + a(7 + a)) = 0 a((7 * -3 + a * -3) + a(7 + a)) = 0 a((-21 + -3a) + a(7 + a)) = 0 a(-21 + -3a + (7 * a + a * a)) = 0 a(-21 + -3a + (7a + a2)) = 0 Combine like terms: -3a + 7a = 4a a(-21 + 4a + a2) = 0 (-21 * a + 4a * a + a2 * a) = 0 (-21a + 4a2 + a3) = 0 Solving -21a + 4a2 + a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-21 + 4a + a2) = 0 Factor a trinomial. a((-7 + -1a)(3 + -1a)) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 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 = -7Subproblem 3
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 = 3Solution
a = {0, -7, 3}
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