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Simplifying (3a + -4)(3a + 1) = 0 Reorder the terms: (-4 + 3a)(3a + 1) = 0 Reorder the terms: (-4 + 3a)(1 + 3a) = 0 Multiply (-4 + 3a) * (1 + 3a) (-4(1 + 3a) + 3a * (1 + 3a)) = 0 ((1 * -4 + 3a * -4) + 3a * (1 + 3a)) = 0 ((-4 + -12a) + 3a * (1 + 3a)) = 0 (-4 + -12a + (1 * 3a + 3a * 3a)) = 0 (-4 + -12a + (3a + 9a2)) = 0 Combine like terms: -12a + 3a = -9a (-4 + -9a + 9a2) = 0 Solving -4 + -9a + 9a2 = 0 Solving for variable 'a'. Factor a trinomial. (-1 + -3a)(4 + -3a) = 0Subproblem 1
Set the factor '(-1 + -3a)' equal to zero and attempt to solve: Simplifying -1 + -3a = 0 Solving -1 + -3a = 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 + -3a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3a = 0 + 1 -3a = 0 + 1 Combine like terms: 0 + 1 = 1 -3a = 1 Divide each side by '-3'. a = -0.3333333333 Simplifying a = -0.3333333333Subproblem 2
Set the factor '(4 + -3a)' equal to zero and attempt to solve: Simplifying 4 + -3a = 0 Solving 4 + -3a = 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 + -3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a = 0 + -4 -3a = 0 + -4 Combine like terms: 0 + -4 = -4 -3a = -4 Divide each side by '-3'. a = 1.333333333 Simplifying a = 1.333333333Solution
a = {-0.3333333333, 1.333333333}
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