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Simplifying (3a + -2)(a + -4) = 6a + -4 Reorder the terms: (-2 + 3a)(a + -4) = 6a + -4 Reorder the terms: (-2 + 3a)(-4 + a) = 6a + -4 Multiply (-2 + 3a) * (-4 + a) (-2(-4 + a) + 3a * (-4 + a)) = 6a + -4 ((-4 * -2 + a * -2) + 3a * (-4 + a)) = 6a + -4 ((8 + -2a) + 3a * (-4 + a)) = 6a + -4 (8 + -2a + (-4 * 3a + a * 3a)) = 6a + -4 (8 + -2a + (-12a + 3a2)) = 6a + -4 Combine like terms: -2a + -12a = -14a (8 + -14a + 3a2) = 6a + -4 Reorder the terms: 8 + -14a + 3a2 = -4 + 6a Solving 8 + -14a + 3a2 = -4 + 6a Solving for variable 'a'. Reorder the terms: 8 + 4 + -14a + -6a + 3a2 = -4 + 6a + 4 + -6a Combine like terms: 8 + 4 = 12 12 + -14a + -6a + 3a2 = -4 + 6a + 4 + -6a Combine like terms: -14a + -6a = -20a 12 + -20a + 3a2 = -4 + 6a + 4 + -6a Reorder the terms: 12 + -20a + 3a2 = -4 + 4 + 6a + -6a Combine like terms: -4 + 4 = 0 12 + -20a + 3a2 = 0 + 6a + -6a 12 + -20a + 3a2 = 6a + -6a Combine like terms: 6a + -6a = 0 12 + -20a + 3a2 = 0 Factor a trinomial. (2 + -3a)(6 + -1a) = 0Subproblem 1
Set the factor '(2 + -3a)' equal to zero and attempt to solve: Simplifying 2 + -3a = 0 Solving 2 + -3a = 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 + -3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3a = 0 + -2 -3a = 0 + -2 Combine like terms: 0 + -2 = -2 -3a = -2 Divide each side by '-3'. a = 0.6666666667 Simplifying a = 0.6666666667Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve: Simplifying 6 + -1a = 0 Solving 6 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1a = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1a = 0 + -6 -1a = 0 + -6 Combine like terms: 0 + -6 = -6 -1a = -6 Divide each side by '-1'. a = 6 Simplifying a = 6Solution
a = {0.6666666667, 6}
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