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Simplifying (2a + -3)(2a + -8) = 0 Reorder the terms: (-3 + 2a)(2a + -8) = 0 Reorder the terms: (-3 + 2a)(-8 + 2a) = 0 Multiply (-3 + 2a) * (-8 + 2a) (-3(-8 + 2a) + 2a * (-8 + 2a)) = 0 ((-8 * -3 + 2a * -3) + 2a * (-8 + 2a)) = 0 ((24 + -6a) + 2a * (-8 + 2a)) = 0 (24 + -6a + (-8 * 2a + 2a * 2a)) = 0 (24 + -6a + (-16a + 4a2)) = 0 Combine like terms: -6a + -16a = -22a (24 + -22a + 4a2) = 0 Solving 24 + -22a + 4a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -11a + 2a2) = 0 Factor a trinomial. 2((3 + -2a)(4 + -1a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 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 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Subproblem 2
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 = 4Solution
a = {1.5, 4}
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