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Simplifying (4a + 2)(2a + -6) = 0 Reorder the terms: (2 + 4a)(2a + -6) = 0 Reorder the terms: (2 + 4a)(-6 + 2a) = 0 Multiply (2 + 4a) * (-6 + 2a) (2(-6 + 2a) + 4a * (-6 + 2a)) = 0 ((-6 * 2 + 2a * 2) + 4a * (-6 + 2a)) = 0 ((-12 + 4a) + 4a * (-6 + 2a)) = 0 (-12 + 4a + (-6 * 4a + 2a * 4a)) = 0 (-12 + 4a + (-24a + 8a2)) = 0 Combine like terms: 4a + -24a = -20a (-12 + -20a + 8a2) = 0 Solving -12 + -20a + 8a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + -5a + 2a2) = 0 Factor a trinomial. 4((-1 + -2a)(3 + -1a)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -2a)' equal to zero and attempt to solve: Simplifying -1 + -2a = 0 Solving -1 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2a = 0 + 1 -2a = 0 + 1 Combine like terms: 0 + 1 = 1 -2a = 1 Divide each side by '-2'. a = -0.5 Simplifying a = -0.5Subproblem 2
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 = {-0.5, 3}
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