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Simplifying 2(2a + 3) * 7(4a + -8) = 0 Reorder the terms: 2(3 + 2a) * 7(4a + -8) = 0 Reorder the terms: 2(3 + 2a) * 7(-8 + 4a) = 0 Reorder the terms for easier multiplication: 2 * 7(3 + 2a)(-8 + 4a) = 0 Multiply 2 * 7 14(3 + 2a)(-8 + 4a) = 0 Multiply (3 + 2a) * (-8 + 4a) 14(3(-8 + 4a) + 2a * (-8 + 4a)) = 0 14((-8 * 3 + 4a * 3) + 2a * (-8 + 4a)) = 0 14((-24 + 12a) + 2a * (-8 + 4a)) = 0 14(-24 + 12a + (-8 * 2a + 4a * 2a)) = 0 14(-24 + 12a + (-16a + 8a2)) = 0 Combine like terms: 12a + -16a = -4a 14(-24 + -4a + 8a2) = 0 (-24 * 14 + -4a * 14 + 8a2 * 14) = 0 (-336 + -56a + 112a2) = 0 Solving -336 + -56a + 112a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '56'. 56(-6 + -1a + 2a2) = 0 Factor a trinomial. 56((-3 + -2a)(2 + -1a)) = 0 Ignore the factor 56.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 '(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 = {-1.5, 2}
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