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Simplifying (2a + 3)(3a + -4) = 0 Reorder the terms: (3 + 2a)(3a + -4) = 0 Reorder the terms: (3 + 2a)(-4 + 3a) = 0 Multiply (3 + 2a) * (-4 + 3a) (3(-4 + 3a) + 2a * (-4 + 3a)) = 0 ((-4 * 3 + 3a * 3) + 2a * (-4 + 3a)) = 0 ((-12 + 9a) + 2a * (-4 + 3a)) = 0 (-12 + 9a + (-4 * 2a + 3a * 2a)) = 0 (-12 + 9a + (-8a + 6a2)) = 0 Combine like terms: 9a + -8a = 1a (-12 + 1a + 6a2) = 0 Solving -12 + 1a + 6a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -2a)(4 + -3a) = 0Subproblem 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 + -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 = {-1.5, 1.333333333}
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