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Simplifying 3a(a + 4) + -2(a + 4) = 0 Reorder the terms: 3a(4 + a) + -2(a + 4) = 0 (4 * 3a + a * 3a) + -2(a + 4) = 0 (12a + 3a2) + -2(a + 4) = 0 Reorder the terms: 12a + 3a2 + -2(4 + a) = 0 12a + 3a2 + (4 * -2 + a * -2) = 0 12a + 3a2 + (-8 + -2a) = 0 Reorder the terms: -8 + 12a + -2a + 3a2 = 0 Combine like terms: 12a + -2a = 10a -8 + 10a + 3a2 = 0 Solving -8 + 10a + 3a2 = 0 Solving for variable 'a'. Factor a trinomial. (-4 + -1a)(2 + -3a) = 0Subproblem 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 + -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 = 0.6666666667Solution
a = {-4, 0.6666666667}
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