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Simplifying (2a + -4)(3a + 12) = 0 Reorder the terms: (-4 + 2a)(3a + 12) = 0 Reorder the terms: (-4 + 2a)(12 + 3a) = 0 Multiply (-4 + 2a) * (12 + 3a) (-4(12 + 3a) + 2a * (12 + 3a)) = 0 ((12 * -4 + 3a * -4) + 2a * (12 + 3a)) = 0 ((-48 + -12a) + 2a * (12 + 3a)) = 0 (-48 + -12a + (12 * 2a + 3a * 2a)) = 0 (-48 + -12a + (24a + 6a2)) = 0 Combine like terms: -12a + 24a = 12a (-48 + 12a + 6a2) = 0 Solving -48 + 12a + 6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6'. 6(-8 + 2a + a2) = 0 Factor a trinomial. 6((-4 + -1a)(2 + -1a)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve: Simplifying -4 + -1a = 0 Solving -4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1a = 0 + 4 -1a = 0 + 4 Combine like terms: 0 + 4 = 4 -1a = 4 Divide each side by '-1'. a = -4 Simplifying a = -4Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 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 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Solution
a = {-4, 2}
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